Comment by tremon
Rental income should not be the primary reason for housing to be built in the first place, so I don't buy that argument. The primary reason to build housing should be demand for home ownership. The volume of housing that ends up on the rental market should only be a small fraction of the total volume.
Instead of rent control, I propose a forced buy-out model: if the current tenant can manage to buy the home they're currently living in, the landlord is not allowed to refuse the sale. And banks are not allowed to deny such a mortgage if the monthly installments amount to less than the current rent.
Again, you are just discouraging people from building more homes. People like to create financial Rube Goldberg machines to address high housing prices, but the solution is simple: Add supply.
Now adding more supply is not trivial in many cases, but at least people can work on the correct problem to solve once it's identified.