Non-luxury housing is already being rented at market rates, except for the rent-controlled units, but those are effectively not part of the liquid housing market anyway because the tenants won't leave. Hence the recent increase in landlords trying to force the tenants out, so the housing can be rented at the market rate, like all other housing already is.

Everything I wrote presupposes that all housing is rented at the market rate, including the non-luxury housing.

I suppose you put quotes around "market rates" as a form of sarcasm, but aside from rent-controlled units, all housing rents at the equilibrium market rate determined by supply and demand. If someone jacks up the price of older apartments and is still able to find tenants, all that proves is that those apartments had been rented out at a price below the market rate before now. The market rate is quite simply the amount people are willing to pay.