1. Depending on how it's handled it might turn into an internal power struggle.
But if Legion wins then Caesar will set up his synthesis(?) which will be compromised of both Legion and NCR qualities. So during this time Lanius might have been killed already, or maybe demoted, or maybe a new system has been set up, or maybe Caesar has found his true successor?
Lots and lots of variables.
2. Never said that House stagnate anything, he won't.
I'm saying that humanity "overall" will stagnate with a few isolated exceptions, like Vegas.
Core Region and the rest of the west coast will continue living under NCR's awful rule and sooner or later fall apart creating a Fallout 1/Fallout 2 anarchy/lawlessness again.
And Legion would be pushed back, putting a hold to their conquest for a long time and during that time something might happen and they might fall apart too.
With House in charge the rest of the world around him falls apart or stagnate as his Mojave stands there as a jewel in the wasteland.
At least until the next super power is born or arrives to the areas, but what is the probability of them being any more successful than NCR or Legion was?
1. True, but I was pointing things out on how they'd play out in the NCR/House way.
2. I think your problem with NCR is a bit misinformed, the war in the Mojave isn't NCR's war, it's Kimballs war. Once Kimball is killed or if Kimball lives to NCR's defeat at Hoover Dam, he is publicly disgraced and thrown out of office, and senators likely to stand up to Kimball's overly nationalist ideals will change their ways to a more Tandi-esque NCR again. Also, on the assumption House wins, NCR and Legion lose the battle, but not the war. When House rises to power, you essentially have three very huge snarling alpha dogs. All fighting for control. House will continue to defend Vegas, as he has no interest in expanding, and the battle between the Bull and the Bear will ever continue until only one remains standing. In alot of ways, I think, unintentionally, their nations symbols represent themselves. The Bear is very strong and will always win at some point in time, and a bull has a very powerful attack with it's horns, but will someday meet a foe it cannot truely beat, the NCR is the Legions foe it cannot beat.
@Schneidend- House actually does tame the region, if you ignore the Fiends, House sends in the Securitrons to wipe them out, successfully might I add.