[habosa]

In a theoretical economy, maybe. In reality you'll have a small increase in wages, but likely business owners being chronically short staffed, going out of business, or choosing not to start a business. Even if wages to go up perfectly like in an econ textbook, that will increase the cost of goods and services which may not matter much for the wealthy residents but will make the city much less attractive for visitors/tourists and cut into the elevated wages. Remember, workers are consumers.

There's also the issue that raising wages will not fix the problem if landlords capture the wage increase by raising the price of housing. It's all about buying power, the absolute numbers mean nothing.

The free market can't solve all of our problems, and even if it could housing in particular is too important to wait on supply and demand forces to fix everything. Moving has very high material/time/emotional costs and humans need uninterrupted housing to maintain a decent life.