That's fine. A neighborhood full of high rises that no one wants to pay to knock down to build taller is naturally full. The government hasn't declared it to be full the way we do today.
> Of course, without government-imposed zoning laws, you will also have residential units competing with commercial and industrial ones, too...
Zoning isn't terrible. Density restrictions are terrible. They are explicit exclusion. They are the direct cause of our increasing economic segregation.
> Oh, and who will take care of the extra infrastructure that is required for more people?
Urban infrastructure is cheaper than suburban infrastructure. We're spending more money on infrastructure today than we would if we stopped excluding people.
> It would also be pretty effective at inducing more rich flight from urban areas into the suburbs
This just isn't true. Tons of wealthy people want to live in dense urban neighborhoods. That's why they're so expensive. What we should change is allowing people with different amounts of wealth to live in the same neighborhood. Density restrictions make mixed-income neighborhoods illegal: only the highest bidders get scarce homes, so families are forcibly sorted by income into separate neighborhoods.
If rich people truly don't want to live in mixed-income neighborhoods, they are the ones who should leave. We shouldn't force others out for their benefit. We used to do that. Now we're doing it to even more families. We aren't repeating the mistakes of our forefathers, we're outdoing them.