That's largely because the basic necessities of living (housing, clothing, food, transportation) are needed in roughly the same amount by all people, and don't scale with class/income/wealth. I live in a 1-bedroom apartment and eat about three meals a day and wear jeans that cost about $50. I have friends who make an order of magnitude more and less than I do. They don't live in a 10-bedroom or 0.1-bedroom place, respectively. They don't eat 30 or 0.3 meals a day, respectively, and their meal themselves don't cost ten times more or less - maybe there's a factor of two or three. The ones who make ten times more than I do might occasionally buy $500 jeans, but even they won't wear it for everyday use, and the ones who make ten times less generally don't buy $5 jeans either.

So, demand is roughly the same from everyone / doesn't scale very much, and the rich can afford to pay quite a bit more. So a market that has rich people in it will have a higher cost of living.

If you want to stop this, the obvious solution is to prevent income inequality (in all its forms - Paul Graham points out, correctly, that this would require us to rethink the very idea of for-profit unicorns - see https://twitter.com/paulg/status/886953410356011008 and https://twitter.com/paulg/status/645343476662427648). Useful tools include extremely high wealth and income taxes. (And, as someone who by any objective standard makes a lot of money, this is why I'm personally in favor of my own marginal tax bracket being 90% or higher - because it means that people who make even more money than I do can't as trivially outbid me for housing, etc.)