Your post assumes that the point of rent control is to provide some housing inventory that is below market value for new tenants. In actuality, the point is to ensure that long-time residents will not be swiftly priced out of their communities.

i.e. it doesn't matter that I'll pay market rent for a rent-controlled unit I move into today. What matters is that the yearly increase in my rent will probably not outstrip my income over the long term.