Absolutely, but it's easier to build quality mixed use development and walkable, bikable neighbourhoods when you don't have thousands of NIMBYs screaming down every proposal.
"This solution won't work in <ludicrously overextended case>, therefore let's do nothing!" -- common software engineering requirements management technique
Go read about the history of paris. One government minister bulldozed most of the city to create what the world now loves. At the time many people wept for the loss of what paris had been (described as a that commercial street in Harry Potter a quaint, magical village that stretched on in any direction). Paris has now created business districts in the suburbs. But even they are are building single family housing instead of the low rise blocks everyone loves in paris core.
Single-family homes are built out in the suburbs. In the city proper, they build multi-story buildings. There are SFH inside the city limits, but these are old, and I'm not aware of any such new developments.
But the thing is, just like elsewhere, much fewer people actually want to live out in the suburbs, which is reflected in the price. Because getting to Paris proper sucks if you don't have a direct rail connection (which most of the outer 'burbs don't), and even then, you're likely to waste hours commuting, between the unreliable service and just sheer distance. Things are improving for "mid-distance" suburbs, but we're not quite there yet.
I live in one of the most populous metropolitan areas on the planet because it's the best place to live in the world. Increasing density and population is working great so far; maybe it won't scale all the way to 8 billion, but as and when there's a problem we'll deal with it.
... I'm talking about building new cities, which seems like the exact opposite of what you're describing?
Anyway, as far what happens when you make renting impossible (or just de facto not financially realistic), in Amsterdam it led to a lot of rentals being sold. The people buying had roughly 2x the income of those renting, on average. So, I guess that's a good thing, if your goal is to evict lower income renters so people can buy a place more cheaply. https://www.youtube.com/watch?v=t05cFv02pzY discusses this at length.
