When the game starts the "Minutemen" are basically just one guy and at the end they destroy the institute or take down the Prydwen, that simply doesn't make sense. At first I though their job were just holding enemies up until additional forces could, like the real Minutemen, that would have made sense, but they basically do everything on their own.
The BoS is basically a science cult, that has real scientists and real scientist_computers, but when this mechanic guy anolysis the same holotape, he suddenly finds a better way to defeat the institute. They don't even have a proper command structure. They are just a bunch of people who are solely driven by their vague sense of justice.
It doesn't take much to take an airship down, but they would never be able to fend off the brotherhood, especially if you consider that howitzers don't work very well against aircrafts.
The Railroad is a different case, they use guerrilla tactics and have a real cause: combating slavery.
And if the institute wished to destroy them, they could easily infiltrate them with some gen3 synths.