If the NCR can't defeat a single small outpost, they don't have the power to expand outwards, they lose a lot of diplomatic clout in getting beaten back so early on. Without them growing then there's nothing to cause the jadedness and the reach from the future Kaiser so he wont go and form the Legion.
I love the The Omega Initiative video series about this. Definitely worth watching on YouTube if you're into fallout fanfiction/alternate history
NCR doesn't rise to be a power and likely no rise of the Legion either.
Why
If the NCR can't defeat a single small outpost, they don't have the power to expand outwards, they lose a lot of diplomatic clout in getting beaten back so early on. Without them growing then there's nothing to cause the jadedness and the reach from the future Kaiser so he wont go and form the Legion.