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Otherwise, they'd lower the price to whatever someone can pay.

Not necessarily. You'd have to look at vacancy rates. But even a city-wide statistic won't be very useful because it looks at low- and high-income units alike. Fancy new buildings have higher vacancy rates due to higher prices. If you had some way to isolate the vacancy rates of high-income buildings, I think you'd see there are quite a few vacancies.

So if a lawyer cannot afford the rent, who can??

Lawyer salaries are not universally high. The idea that lawyers make a lot of money comes from the top lawyers. Don't look at "average" lawyer salary, as the mean of a set of data can be heavily skewed by outliers.