The BoS still survive if you destroy the Prydwen, you've just destroyed the command of the Capital Wasteland chapter. Hell they still show up in Vertibirds, so apparently they have a backup staging area just outside the Commonwealth. What you do is essentially kill off their WH40k imperium of man aspirations.
The Railroad seems as if it was the first faction that was worked on. You can do almost their entire questline before even doing the main story. And then, after the main story the radiant quest line up changes from putting up MILAs and clearing locations, to delivering care packages and taking down coursers. As well as a short questline about taking down the Railroads next biggest threat, the Raider leaders. And you get access to the BoS vertibird grenades.
After the BoS is over, they give you a quest to make reactor coolant, nothing else changes. Maybe I could get a grenade to call in a fully loaded gunship with knights as backup on it? no? nothing? okay. Well at least they sell you some decent armor and weapons.
If you side with the Institute? Nothing changes, you get the same radiant quests you got when you joined. I think the vendor starts selling relay grenades and you get Fathers lab coat. The scientists ask you whether to work on Synths or Weapons, I went to test it and nothing changes. Synths still spawn with the same weapons as normal, vendor still offers the same weapons.
The Minutemen only have radiant *insert enemy* is attacking the castle after endgame. Everything else is the stuff you get during a normal playthrough.
Pretty much.
The Minuteman being so generic is partially deliberate. They are the "neutral" faction of the four, though depending on how you play,you can have them remain neutral or shift their alignment to that of the faction you choose to ally them with.
In universe, they really only have one broad goal, and that's to serve as the Commonwealth's standing army against threats to its people, and all that changes depending on your allying with another faction is that the other factions goals get tacked onto that.
The Institute is slightly disappointing I admit, but it does make some sense you having a limited amount of control over their activity, as Father was basically the big picture guy while the other departments could pursue their own projects with a very free hand. It's even mentioned, if you check out their lore, that the Director position is effectively limited to "ensuring the well being of the Institute as an entity", they don't really have much say on specific sub-directories, who are free to pursue their own projects so long as they don't endanger the group.
Given their scientist oriented ethos, it does make conceptual sense.
The Railroad being so narrow storywise is also logical. They really have only one goal, and that's to put a stop to Synths being used by the Institute as slaves. They don't, as a whole, give a flying fuck about anything else. In fact, it's only when their back is to the wall and they're up shit creek without outside help do they swallow their pride and go seek the Minutemen for the army they'd need to achieve their goals.
The Brotherhood petering out after the Institute is gone and their post main goal quests being ho-hum is also logical. All they are there for is two things: Stop the Institute and tap the Commonwealth of it's technological salvage.
Once the first goal is met, the second, which has no definitive end, basically gives them the excuse to stick around, but doesn't really give the player much more to do for them.
I'm kind of glad the cut the option to become the Elder of the Brotherhood since it would have been the normal business as usual only Kells or Danse give you orders. I prefer the idea of being the highest ranked soldier with permission to do whatever you deem worthy to advance Brotherhood goals.
I do think if they want to keep forcing you to become leader of a faction they need to have it so that isn't the end of the storyline and you actually need to lead your organization through some sort of crisis and have your choices matter. After that they can still give you the option to do grunt work or delegate it as you see fit.
Technically, they cut two paths, one of which can be revived with mods.
One allows Danse to challenge Maxson for the position of Elder and take over. This was cut before they went anywhere too definite with it, and there's not too much in the game files to really integrate it into the finished product without throwing the BoS plot off it's axis, and what's left in the game files are mere fragments anyway.
The second is basically you becoming SENTINEL (not Elder) if you used the Minutemen to take down the Institute, and left the BoS out of it entirely before you were forced to take sides definitively for or against them (best time to do is after Blind Betrayal). A mod restores what is basically Maxson being a little annoyed you didn't involve the Brotherhood, but admits you did get the job done and the Brotherhood didn't have to shed too much of their own blood to do what they came there to do as their primary goal (kill the Institute), so while unorthodox and not according to how he planned it out, he'd have to be an ungrateful jackass to not acknowledge what you pulled off so you become a Sentinel, which is basically one step below him and you basically outrank everyone else.
Here's the mod that re-enables this:
https://www.nexusmods.com/fallout4/mods/12183
This does have the consequences of the Brotherhood being a mix of "really sucks we didn't get to kick the Institute's ass" and "well, at least it was a clever way to get the job done with minimal casualties", which is opposed to how the BoS practically deify you as a badass if you did the pure BoS path.
There is also mod that let's you avoid becoming enemies with Railroad while still remaining friends with the Brotherhood, basically involves talking Captain Kells out of saying "let's kill the Railroad just to make sure they don't make our lives suck later":
https://www.nexusmods.com/fallout4/mods/20330
If you manage to talk him out of it, the game skips the quest where the Railroad has to die at BoS behest, though you can still piss the BoS off later by siding with the Institute or otherwise helping the Railroad in such a way it still put you at war with the BoS later (they left in a way to do this even if you talk down Kells with that mod, clearly Bethseda anticipated this possibility).
