I'm not sure I want to be a part of House's "progress" if it leaves the majority of humanity in the shitter.
I do.
The NCR tried to take the approach you are espousing and it is failing for them, they are about to enter a food crisis, they are embroiled in a catastrophic Vietnam style scenario in the Mojave, and people are jumping off the sinking ship.
Once the ship is sunk, and the NCR just crumbles out a plethora of failures, food shortages, military humiliation and crisis, high taxes (most likely with a healthy dose of rebellion), the welfare state will collapse, so will the economy, jobs will disappear, and the NCR will have shoved 800,000 people in the toilet bowl.
None of these problems exist with Mr House, because of his small world approach, renovating Hoover dam, stabilising the New Vegas area, getting into space technology again, and making sure humanity is going in the right direction under competent leadership
You keep saying how it will be so shitty, but you aren't explaining why. What factors will make it shitty? Who will be doing the shitty things? Who will be stealing the lives/possessions/freedoms (almost don't exist in Legion territory). You aren't specifying where these issues will come from if Caesar dies, you have no evidence for your claims so I am not gonna treat it as a valid argument.
Since when were people in Legion territory the majority of humanity? Your forgetting Canada, Alaska Mexico, Europe, Asia.