Whilst I agree with your comments the greater point I was making was that in the current climate the 'silver-bullet' has to contain a number of elements in order to have any long term effect.
But rent controls shouldn't be one of those elements.
You could even make the problem worse in respect of supply - my making it less attractive for investors to build houses.
You will certainly make housing quality worse, by making landlords more reluctant to invest in maintaining/improving the standard of their house. If they are stuck charging a below market rent in an undersupplied market, then there is a much reduced incentive for them to invest in the habitability of the house, as they won't see it reflected in either the rental or tenant retention.
You will also make it harder for some marginal tenants (larger families, people with pets, people with poor english) to find houses - why rent to someone with a large dog that can damage the property, if there are fifteen other prospective tenants who don't have dogs and you are required to charge them all the same.
Finally, as another poster has pointed out, these regulations never work well. People find ways around them.
It's all very well to want to fire a silver bullet, but you need to make sure the gun is pointed away from you.