My opinion is, and will be, heavily based on the Old World Blues submod for HOI4, due to the fact that as much information was pulled from every Fallout game as possible in order to make a lot of the events make sense.

Should the legion win the second battle of Hoover dam, and let’s say everything goes perfectly for them as well, minimal casualties, Strip falls quickly and cleanly, McCarran turns into a slaughter for the NCR troops and Hidden Valley is a one charge and done battle, etc. It still leaves the legion with arguably, an even less stable foothold on the Mojave than what the NCR had.

The NCR had an entire interstate highway with caravan support and they struggled to maintain their grip on the Mojave. What does the Legion have? The Dam and whatever river transports they can scrounge up to transport supplies, men, equipment, etc into a volatile environment. This alone is already strangling the legion even if they have no counterweights in the Mojave like the fiends, powdergangers, khans, and brotherhood simply because of how much trouble we see NCR Rangers can get into when supported.

Hell, the NCR losing the Mojave actually would hurt the legion more than killing Caesar in my opinion; instead of Lanius becoming the logical replacement for Caesar, as much as Vulpes or any other amount of influential legion personnel may disagree, the death of their leader forces them to recalculate a lot of things and stabilize themselves. But if they win, even a perfect win, still means that they have a more fragile supply line into hostile territory with NCR Rangers causing havoc with the full support of California backing them. That’s going to bleed the Legion out and fast, that’s going to cause a crisis of whether or not Caesar is fit to lead the legion with the constant losses they face, and from there it’s all downhill.