> because too many people want to live near each other
Your market analysis is incomplete. For example, http://www.theguardian.com/business/2014/feb/01/rich-oversea... says "only 27% of new homes in central London went to UK buyers, while more than half were sold to residents of Singapore, Hong Kong, China, Malaysia and Russia." These are not people who live there, but want to invest in the London real estate market. By taking housing out of the market, they also increase the market rates through artificial scarcity.
> if not price then what
Different taxation for residents vs. non-residents. Rich people tend to have large places, so taxation based on square footage per resident. Set up building requirements that give preference to low-cost housing. There are many ways to tweak the economic landscape.
> If you set up your lifestyle ..
You make it sound so easy. Why not just set up your life to earn another $100K/year?
> you must be doing something fantastically productive
Why does that follow? If I inherited my $1 billion, I'm certainly able to afford a quaint $10 million penthouse in San Francisco even if just leave the money in an index fund. If I am a dictator who funneled money out of the country into my personal foreign bank account, leaving the country in poverty, would you say I was productive? Or if someone discovers oil on my land, and I exchange the drilling rights in exchange for 1% of the extracted revenue, making me rich enough to, say, move to Beverley Hills, was I really doing something fantastically productive?