First off, why is the Legion bad for fighting the NCR and the NCR good for fighting the Legion?
Legion attacked the NCR last I checked not the other way around. You suggested I should support the Legion because they bring civilization, terrible though it may be, much more swiftly but they're attacking the one area of the country that is definitely not in need of civilizing because Caesar wants his synthesis. Why should I support that?
The Legion brings safety and order to chaotic lands in a very short timespan, while the NCR throws its own people into the fire and sometimes even abandons them (Camp Guardian) just to make profit, how is that better?
Because the NCR's idea of civilization doesn't accept slavery, r@pe, torture, brainwashing, absolutism, misogyny, a luddite like refusal to use any technology that people may become too dependent on (whatever that means), and so on. And the reason the NCR is overstretched in the Mojave, as stated time and again, is because of the Legion draining all it's resources. So if the game offers me an option to remove that obstacle why wouldn't I take it?
The NCR is not the ideal nation to civilize the wastes, because they are inept. The Legion does the dirty, mean, and tough things that need to be done for the future, there NEEDS to be a unifying force, the NCR doesn't care about bringing civilization, it cares about annexing land to get richer and making the people back home happy, and not about uniting the wastes.
So inept they've created a massive functioning nation state from a single small village in less than a century.
Okay so explain to me why the dirty, mean, tough things the Legion does need to be done for the future. Why does the unifying force have to be Caesar's Legion? Why is an autocratic, fundamentalist state that has yet to weather a single change of leadership and that is overwhelmingly dependent on the quality of that leadership the better choice in the long term?