So then how would you frame Vatican II? What was it's purpose, what did it change (and why) etc?
To really answer this we need to nail down what Vatican II actually changed. Fortunately I found a handy list of the big points, so I'll go over them and give my take, but first a preface.
Preface: I'm not the world's greatest apologist, and I can be wrong about things. I recommend you also consider the words of more accomplished apologists. If you go to YouTube and search "Bishop Barron Vatican II" you'll find a whole bunch of good videos on the subject.
With that out of the way, here's my take on a change by change basis covering the big points in three categories. The first sentence is the summary provided by the list, my take follows it.
Category the first, Liturgical changes, these are changes to the form, but not the function, of the Mass and mark the distinction between the Traditional Latin Mass, or TLM, and the Novus Ordo Mass, or NO.
Vernacular Mass: Mass was no longer exclusively in Latin; priests could celebrate Mass in the local language, encouraging greater participation from the congregation. As I understand it this change, like most of the Liturgical changes, was to make the celebration of Mass more accessible, understandable, and engaging for the congregation. Instead of going to Mass and hearing the Priest conduct the service in a language you don't know, now its in your native language so you can understand the words which begets giving them more thought and impact. Despite what some claim this change did not eliminate the Traditional Latin Mass, which is still practiced every week in many Churches.
Priest Facing the People: The priest now faces the congregation during the Eucharistic prayer, emphasizing the community aspect of the liturgy. Also known as versus populum as opposed to ad orientum when the Priest faces the same direction as the congregation. As above this was intended to make the mass more engaging for the congregation, not much else to say about it off hand. I have seen Mass where the Novus Ordo is conducted ad orientum too.
Expanded Readings: The number of readings during Mass increased, and the church now cycles through all four Gospels over three years. Bringing more of scripture into Mass and adding the cycle to reduce repetition is one of the changes you never hear any complaints about. I like having more scripture and less repetition in Mass.
Revised Sacramental Rites: The rites for the sacraments were revised, and the Rite of Christian Initiation of Adults was reformed. This change has no effect on the theological nature of the Sacraments themselves, merely how they are celebrated, and it was done to emphasisize their communal nature. This is very much in line with the overall theme of making things more accessible, understandble, and engaging. The revival and reformation of RCIA was hugely important and has helped countless adults convert to Catholicism in the decades since.
Simplified Liturgical Calendar: The liturgical calendar was simplified. Honestly this could warrant its own sublist but this post is going to be long enough already. Still in line with the theme of making things accessible and engaging, without getting into the weeds of what specifically was changed about the liturgical calendar, what I find noteworthy is that these changes put more focus on the Christ. The new liturgical calendar is designed to lead believers through the mysteries of Christ's life, from Advent to Pentecost and Ordinary Time over the course of the year.
Active Participation: Emphasis was placed on the active participation of the laity in the liturgy. Leaning in heavily on the engaging aspect of the overall theme this change makes the congregation more of a part of mass than before.
Next we have the Doctrinal and Theological changes, which makes them sound more impactful than they really are, and thus they are often the ones people try to twist into being scandalous when they aren't.
Religious Freedom: The council affirmed the right to religious freedom, a significant shift from the Church's previous stance. This is not the Church saying it's okay to not be Catholic. This is the Church saying that, because God gave us all free will, you have the right to use that free will even if it means you're wrong. This is a formal culmination of a shift that had been ongoing for over a century by the time of Vatican II. It used to be that the Church would persecute people for apostasy, you saw this in things like the Inquisition, and events surrounding the Reformation and Counter Reformatiom. The underlying principle in the shift away from such persecution is that no one truly comes to the Lord by force. This affirmation brings the Church more in line with God, because God would rather have true and honest believers than people who are pretending out of fear of persecution.
Ecumenism: Vatican II promoted ecumenical dialogue with other Christian denominations and religions, fostering greater understanding and cooperation. This goes hand in hand with the previous change and is somewhat more self serving than it might sound. Again this is not the Church saying that other denominations are any less wrong, but since we are acknowledging people have the right to be wrong, we should also be reaching out and trying to work with them in their wrongness instead of shunning them. Furthermore by increasing understanding between the denominations we might be able to curb the rampant anti-Catholic sentiment and propaganda spread by protestants, most of which is rooted in a poor and misleading concept of Catholicism.
Relationship with Judaism: The Church's relationship with Judaism was redefined, rejecting the traditional accusation that Jews were responsible for the death of Christ and condemning anti-Semitism. This is the one that gets all the conspiracy theorists riled up but it's not what they make it out to be. To some degree it is a response to WWII, and the allegations of the Holocaust, which at the time of Vatican II was considered completely factual. However the more important part of this is purely theological and grounded. While the notion that Jews killed Jesus makes for a spicy meme, theologically its completely missing the point. Christ didn't die because the Jews wanted him to die, Christ died for our sins; Christ died to redeem us all. To reduce that act down to the work and responsibility of the Jews is a gross devaluation of the truth.
The Church as the "People of God": The Church was described as the "people of God," emphasizing the role of all baptized members in the Church's mission. This can be summarized as calling people to live their faith more actively. It goes along with the Liturgical changes above, now that mass is more accessible and understandble, we should take it's lessons and apply them to our lives.
Role of Bishops: The role of bishops was given more weight, and the concept of collegiality (shared responsibility between the Pope and bishops) was emphasized. Really this is less of a new change and more of a return to the way things used to be done. The Pope is supposed to be the first among equals with the rest of the Bishops, and this change brings us back to that.
Lay Ministries: Lay readers and lay ministers of Communion appeared during Mass; Laity were represented on parish councils and diocesan boards, and lay men and women, many with theology degrees, replaced clerics in a number of administrative church positions. Sticking with the overall themes again, now that the laity has a more accessible faith that easier to understand the Church wants to offer them more ways to engage with it not just at Mass but in general. As an added benefit this increases dramatically the pool of people the Church can call upon for help in its administrative needs.
Finally we have a third category to catch some other notable changes that don't fit the first two categories.
Social Communication: The council addressed the role of media and social communication in the Church's mission. This is the only of these changes that really matters. By the time of Vatican II it was clear that media was going to be an increasingly important part of people's lives. New technologies like Radio and Television were having profound effects on people so the Church had to formalize its own approach to such things. A driving force of this change was the work of Blessed Fulton Sheen, who hosted a his own Radio series called The Catholic Hour and then a Television series called Life is Worth Living before Vatican II happened. Sheen's work showed the Church as a whole that Radio and Television could be used very effectively for the good of the Church and the people.
New Catechism: A new Catechism of the Catholic Church was developed to reflect the teachings of Vatican II.
Revised Canon Law: The Church's canon law was revised to reflect the changes brought about by the council.
I'm grouping these last two together because there really isnt much to say about them beyond what's on the tin. Vatican II changed some things, so lets make sure our teachings and laws reflect those changes. Simple as.
If it was necessary in 1958 in your mind, then why wasn't it necessary in 1858 (or 1758.. ). What changed, that caused the Church to take whatever steps (as you define) were taken during and after Vatican II?
First of all, Vatican II was 1962-1965 not 1958. Second necessary is a strong word, and its hard to really quantify in terms of my mind because I wasn't alive before Vatican II so I don't have that frame of reference in a personal sense. Besides it's hardly my place to say how necessary such things are or aren't anyway. In a more general sense the world is constantly changing, the Church has to find a balance between maintaining tradition and adapting to modern life so it can deliver the value of that tradition to the people. I think the previous section did a good job of making it clear that the themes of Vatican II were accessibility, understanding, and engagement. As for why these changes didn't happen one or two hundred years I would say the most logical reason is that previous councils had more important matters to discuss than the relatively minor changes in Vatican II. Prior to Vatican II the most recent council was Vatican I, which occurred from 1869 to 1870. Prior to that we have to go all the way back to 1500s for the Council of Trent which was 1545-1563. For a more tangible example though consider the point on social communication. The Church could not address the role of new technologies like Radio and Television in it's mission before such technologies were invented.
I am asking in good faith, albeit in a jaded way, because anytime the subject comes up - as I mentioned earlier in this thread, there is a move to suppress the discussion or hand-wave it away as unimportant. Except, the Church clearly thought it was quite important. Why - and equally important, why then? What changed?
Honestly I believe the hand waving or suppression you're referring to is largely reactionary. People are tired of Vatican II being blamed for everything and made out to be some massive conspiracy when it's not. So many people ask about it bad faith that the ones who are genuine get drowned out in the noise. Really Vatican II is just the most recent in a series of 21 Ecumenical Councils that have occurred in the history of the Church.
Here's a nice summary of what each Council did. As for why, the Church is arguably the largest and most important organization in the world and it bears an immense responsibility. Thus these councils serve the important function of maintaining internal cohesion, assessing how well that responsibility is being fulfilled and making adjustments to fulfill that responsibility better in the face of an ever changing world.