Sure, the factions all had more flaws than good points, but people's attitudes towards the Brotherhood of Steel felt unique to me. They were actually making up arbitrary reasons to justify why they were going on with supporting arguably the most xenophobic and destructive faction in the game, all while chanting them on as saviours. It seems like just normal stuff, but when you really think about it, they're channelling the Brotherhood themselves, moving through their actions without once realising what they've done. And in a way, the Brotherhood were channelling a lot of the modern FPS gaming attitude and subsequently the modern attitudes towards politics as a whole.
I would say that, for all the stupidity and ridiculousness Bethesda injected into the game, at least this form of unintentional meta commentary is commendable.
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Anyways, back to the other factions - taking a look from the bright side, (or as I call it, the if Obsidian had made the game side) they have points that do make sense.
The Minutemen would be doing their protect-the-people and rebuilding work off-screen, all the way to the off-map areas of the Commonwealth. In a way, the fact that they're an organisation with the most busywork (got another settlement for you) but the least rewards, shows why they failed in the first place - no one was willing to support such a bum deal. The Minutemen are basically a charity PMC, a concept that just doesn't work in the post-apocalypse.
We should've been allowed to change how it all worked, possibly affecting the reputation of the Minutemen as a whole.
The Railroad rescues both normal slaves and Institute synths, but turned directly towards synths once they realised the Institute harmed far more than anyone predicted they would, and that they were a growing threat. They themselves realise that their objective is a bit more pointless than the other factions, plus, Desdemona herself doesn't mind if you tell her you're not particularly willing to see synths as equals.
To me, they felt like they would've worked better as a side-faction that you can integrate with the Minutemen, and not as an actual faction.
The Brotherhood are just pre-emptive strike dicks, who assumed that just because the Institute had a large power source meant that they were going to get attacked across the state. A reminder of real-life "Old World" politics, where a lot of wars are due to pre-emptive attacks. Remember, Maxson himself might not be as fanatical as he appears, but might have to appear so for obvious reasons. The Brotherhood good-guy knights has just reintegrated the West Coast styled Outcasts back in, and now he has to please both sides. As a result of bureaucracy and compromises, he appears conflicted and does not make much sense at first.
To me, his true reason for hitting the Institute was to show the Outcasts that he was capable of being a leader who could effectively quash potential threats, not because of anything directly related to the Institute.
Finally, the Institute was created by misguided people with lots of good ideas but had no idea what they were doing. They wasted potential every bit of the way and in addition destroyed everything that was good (they sent armies to destroy one of the biggest settlements in the Commonwealth for a single component, at University Point) along with that. In the end, the results is an organisation that means well, but fails entirely to achieve what they meant to become, and is overall a disappointment to people living on the surface. Everyone you take to the Institute laments on how much of a failure the Institute was to hold the key to rebuilding and just horde it all to themselves.
Ironically, all of the Institute was a good metaphor for what Fallout 4 was. Misguided, wasted potential, unintentionally destroyed the good things, fails to achieve its goals, and overall only looks good from the outside, until you really start to think about it.