That would require far more dense housing.

In general I disagree with this, if we spent a fraction of what we do on car transit on mass transit we'd be able to support mass transit basically anywhere, except large cities with ridiculous spread, like Phoenix.

In particular here though I was just talking about better commuter trains and (the existence of) HSR, neither of which is really dependent on density.

Who would support mass transit? If everyone has the option of low density housing with the luxury of their own cars, they're going to take that option instead of mass transit. The proof is everywhere.

Everyone that lives in the downtown of a city?

Mass transit becomes slow when it has to make many stops and goes for long distances.

NYC subway is only efficient because Manhattan is so dense, and much of areas around it are reasonably dense.

Commuting from further away, like a couple dozen miles into NY or NJ, becomes massively more burdensome, because a train has to go all this distance, and the station is not close to home. Of course, you can spend this hour or two reading, or maybe writing or even sleeping on the train, unlike driving.

That's why you make it multi-track. I grew up in the suburbs of chicago and the rush hour train could take you about 30 miles into downtown in 35 minutes as it just picks you up in the suburbs and then hops over to another track where it can drive the rest of the way without stopping.