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.

Unless there exists _any_ kind of unemployment - in that case people will travel for a ridiculous amount of time just to have a job, thus ruining their chances of a decent private life.

Things do not just adjust themselves as in the theories, weaker people are just squeezed harder. When they can't be squeezed any more, things _may_ change - but when is that?

The working poor are a pretty good example of this.

This is the theory, the practice is that there will never be scarcity since if the real alternative for these people is unemployment, they will still accept punishing conditions (long commutes, long hours and barely making the ends meet).

It's one of the cases where the market is working as expected (low wages since the offer is high), but it doesn't really translate in benefit for (some of) the people involved.