The largest concentrations of wealthy people in the world are in large high density "world cities" (New York etc).

Wealthy people do that all the time. It is called "Living in downtown New York".

The high prices of living in the city prove that people actually prefer to live in high density places.

Why else would they be willing to pay so much money to live there if they didn't like it?

In many cases, it's because they don't want to have to commute in from Westchester every day although certainly some like to live in the city for the cultural opportunities and other aspects of a major urban lifestyle. Of course, no small number of the wealthiest also have a weekend place out in the Hamptons or wherever so they can escape the city. (Which I can certainly empathize with based on the summer I lived in Manhattan.)

To be fair it's possible that they just want to maximize time, which is done by living as close as possible to where they work.

.... Which is a benefit of high density cities, correct?

This isn't particularly a benefit of high-density cities. I work in a fairly low-density city, but some of my coworkers still live close to work. My mom grew up in a small southern town in the '60s, and my impression is that many people there lived pretty close to work.

>My mom grew up in a small southern town in the '60s, and my impression is that many people there lived pretty close to work.

In the 1960s there was approximately half the population in the United States that exists now. The problem is that living close to work and extreme low density doesn't scale. For a majority of people to live close to work, something has to give, whether it be density or perhaps companies allowing telework.

What does one's wealth have to do with how dense of an area in which one prefers to live?