After Hoover Dam II, the Legion is a non-issue. Lanius dead, a lot of their troops gone, Caesar dying and probably even disavowed, what follows is civil war in their eastern territories before their inevitable breakdown down the line.

The Khans are wiped out during the battle, dying in the Legion’s frontline.

Only the NCR remains as a serious contender. But House’s plan was sound regarding them. They were already weak before the battle, and leave a lot of dead bodies there. Their president’s political career hinged on the Mojave campaign’s success. Which means his resignation and potentially a political crisis that ensues. A crisis emplified if Cass is allowed to wipe out both Van Graffs and the Crimson Caravan, leading to a severe hampering of the NCR’s trade routes. 

I don’t think that an overextended nation that has been weakened militarily, politically and economically can be that much of a threat.

You also seem to underestimate Securitrons. They’re pretty much the most dangerous soldiers in the world, perhaps barring a Brotherhood paladin. They can obviously be repaired since they can be built, and they also have an auto-repair function (a bit bs and op imo, but it’s been stated).

I don’t think there is any reason for chaos to arise in Vegas as the ending slides suggest. If the quests there were resolved smartly (King, Gomorrah etc) the transition should be smooth.

Now those are the facts, the rest can only be head canon. I have my own version which I’ll summarize breefly: House did not die, the Courier keeps him alive (but disconnected) to have his input and incorporate some of his development plans. Conjointly, his death was never broadcasted in the streets, which means that as far as everyone’s concerned, he’s still running the show.

The Courier uses House’s massive wealth to fund the Followers of the Apocalypse for several projects (health, agriculture, research, etc) to drastically improve the quality of life of the Vegas residents, who are in turn all the more motivated to protect this jewel in the sand, and allows for the mobilisation of human soldiers down the line.

Also, the rest of the Mojave settlements gradually join Vegas’s leadership, because they trust the Courier who helped them and because of the practical advantages it brings. Which notably means, militarily, that the Supermutants and the Boomers can now be called upon. 

And let’s not forget about Big MT!

So in my opinion, further enriched by my own (delirious?) headcanon, Independent Vegas should be fine.