I'm aware of the justification the game presents, it's just that it comes a bit out of left field with Maxson being shown as a kind of naïve kid in 3 (Expected, since he's like 10-12), and growing up during a period where the two major threats (Enclave and Super Mutants) were already taken care of; so it's a bit hard to bridge that gap. But then again, this is a game written by Emil fucking Pagliarulo, so I fully acknowledge I'm being a bit nitpicky.
I've already bloviated a ton on the Institute and how Fallout 4's plot suffers as a result of trying to force the slavery metaphor. The BoS are possibly a victim of this too. One theory I have (though maybe I picked it up somewhere else) is that 4's plot might've ended up being shockingly similar to 3 at conception, but realised this late into production and so had to course correct shoddily without having to restart the entire thing.
Considering how tiny a part the Railroad play in the story, I theorise they and the Synth focus were given extreme prominence last minute in order to differentiate 4 from 3. Given how similar writers end up being to prior works, I think Emil somehow ended up sleepwalking into creating a more or less identical story to 3, and I'm talking:
1) Family member missing from Vault
2) Rediscovery of family member later on, saved from the enemy
3) Have to seek the aid of X=group in order to combat said enemy
4) The enemy's goals will result in complete subjugation/genocide
But the most egregious part of this is hasn't been said yet. You see, Shaun's kidnapping makes zero sense in the story and ultimately amounts to nothing. Also factor in Kellogg. The Institute have synths and Coursers more than capable of doing the things Kellogg can do. There's no meaningful reason stated as to why Kellogg is given the task, and even his time with Shaun as a child is fake because the Shaun we see him with is the synth version. The Institute also do not shun hiring capable outsiders, it just pertains to scientists mostly because they already have a capable fighting force on hand.
It's entirely possible at some point, 4's plot involved
the Enclave. Maybe the Institute were a front for the Enclave, or a puppet, something that hid from the public at large the true authority in the Commonwealth. It wasn't like the Institute was some secret in Fallout 3, anybody who can be asked about it knows more or less what it is, so people being sceptical it even exists in 4 makes zero sense considering.
The BoS would've been more or less identical to how they were in 3 with the Minutemen giving you a middle of the road option potentially. Brotherhood wanting to bomb the shit out of the Institute versus preserving some of it for the long-term prosperity of the Commonwealth. This'd make the conflict between the Minutemen and BoS more akin to Independence vs NCR in New Vegas, with the Institute/Enclave acting similar to the Legion or House. Making them some front for the Enclave also resolves their desire for genetic purity in Shaun, which is otherwise non-existent in-game itself. It also makes the hiring of Kellogg make more sense due to the Enclave's probable diminishing manpower pool.
Shaun would be a pure genetic outsider raised wholly on Enclave ideals to become their president for life. Kellogg would be a more contentious element as he did actually raise Shaun from baby to adolescent or something which gave him just enough of an outside perspective to make Shaun either redeemable/open to reform or give reason for why he allows you into the Institute/Enclave to begin with. Kellogg not being a thing post-1st half is too big a fumble to attribute to shitty writing. He was a character more integral to a different story entirely, one we didn't get.
Valentine momentarily becoming Kellogg also makes sense in a scenario where the Enclave had a computer president once. We're given the hint in that moment people can be uploaded into synth bodies, but it goes fucking nowhere lmao. Imagine if Nick Valentine was the memory-wiped copy of some Enclave computer-president rather than a police detective with an incomplete case with a retarded as fuck conclusion. Kellogg residing in Diamond City could've been a 2-birds-1-stone scenario of keeping an eye on him whilst raising the heir apparent to the Enclave.
Kellogg's relationship with the Enclave can begin earlier as opposed to the year(s?) long trek to the East coast from the West, since he might go North to avoid the chaos/dangers East of the Colorado river (Caesar's Legion having a low view of NCR citizens or a broken apart Legion of warlord states making him wary, you choose) and end up in Chicago. The relationship and thus trust between the Enclave and him can begin to grow earlier and so tasking him with the capture and raising of Shaun is also made more credible.
The Railroad always felt tacked on compared to the the BoS and the Minutemen. The latter both have grand set pieces, right? The BoS have the Prydwyn and Liberty Prime, the Minutemen get the Fort and artillery. The Railroad get some dingy basement and their mission to blow up the Prydwyn involves just planting charges on the Prydwyn itself versus the grander spectacles afforded by the Minutemen and Institute. The BoS had to be made "meaner" in order to create a contrast between the Railroad and themselves when it comes to synths. The rest is history.
TLDR: I have a theory that the first half of 4's main story (Kellogg, Shaun kidnapping, etc) feel so different from the 2nd half (Synths!!! All the way down! Slaves! Gorillas!) because the story being told by the 1st half never actually got a conclusion, and the 2nd half is of a totally different plot in order to differentiate it more from Fallout 3.