I find theorizing like this when it comes to Bethesda Fallouts is less of an actual theory with evidence to be had/found and more so just us trying to cope with the reality of their writing. Same goes for the theory that the ghoul kid in the fridge wasn’t actually in there since the Great War, but rather since the Battle of Quincy since he doesn’t specify. He doesn’t need to specify, because the Great War is obviously what the writers intended, but the theory serves as a coping mechanism to counter the lack of logic put into that quest.
With the Minutemen, it’s the same thing. There’s no logic to them. They’re Bethesda’s attempt at a faction with historical roots similar to the Legion modeling themselves off Rome, except Bethesda takes the gimmick of the Minutemen’s historical roots way too far. Caesar talks about how everything he did forging the Legion came from the valuable lessons he learned from old books, twisted to his own benefit in this post-apocalyptic world they live in. He models his faction off Rome, but also uses other ideologies such as Hegelian dialectics and the ideas present in fascism to create a stronger hold on his faction that he believes will make up for the shortcomings of the past Roman Empire that fell.
The Minutemen on the other hand are a bunch of LARPers who found a museum and thought a confederacy of settlements was a good idea and that retaking the Castle (which should be obliterated after the war) was awesome because it was the base of the faction they model themselves after. That’s about all the thought put into them. They don’t adapt to the age they live in, rather they believe their morals are unbreakable. When it came to the Battle of Quincy and they are absolutely destroyed by the Gunners after being betrayed by their leader they were destroyed in a snap. Now Preston has to lug around the survivors all across the Commonwealth which he fails to protect most of them, and by the time you arrive to the museum, they’re already as good as dead (of course Bethesda doesn’t allow this, and no matter how long you wait or avoid helping them, they’ll always be fine until you do).
And the moment you help them out, Preston immediately offers the role of General to someone he’s barely just met because he doesn’t have the balls to lead himself. That or he’s just lazy. He isn’t smart or cunning or politically motivated to use the Sole Survivor as a puppet, he’s just another form of Bethesda writing on display.