None of those are really pertinent because it doesn't change the fact that the well-off person is going to occupy an additional housing unit in this scenario no matter what.
The question is whether it's going to be new construction that they occupy or existing construction. If you're not well-off you'd want that decision to end up with "new construction" so you can move into "existing construction" at a lower rent/mortgage than if new construction didn't exist.
I don't think that is necessarily true. I believe there are, for instance, many reasonably wealthy people who live somewhere outside California and would not move into a dumpy old apartment in LA or SF but might move into a fancy new one. In other words, they will not occupy an additional housing unit (in a given market) unless it is "nice" enough.
I am in favor of building new housing, but I'm even more in favor of reducing wealth inequality. I think we can do both, but we need to be deliberate about it.