You are correct that removing rent control would not completely solve the problem. The underlying reason for the increase in rent prices (and thus the need for rent control) is that there is a fixed supply of housing. The city has strict zoning laws that have limited the ability to build up[1]. Without a way to increase the supply of housing the only way for the market to reach equilibrium is for prices to rise.

So to make prices reasonable, both zoning laws and rent control will have to be reworked.

(1)http://www.slate.com/blogs/moneybox/2013/04/11/san_francisco...