I don't have a perfect solution, either, but I see unintended consequence from this:
* Fewer rentals on the market
* More instances of landlords "re-occupying" a place (eg, ACTUALLY kicking out the residents) in order to fix it up (or not) and then re-rent to someone else at a much higher base rent, later.
When rents go up, tenants push themselves out (or, the market pushes them out). When we devise tenant protection laws, we invent 'better' landlords who find clever ways to PUSH out people who are paying below market.
If there was a way to artificially hold ALL rents down, it might be less obvious -- but under a rent control scheme, everyone knows when you're paying below market; you look at the classified ads (okay, craigslist) and see that you could never afford to find a 'new' place like yours at the same price. The tenants know it, the landlords know it. The tenants have protection. For awhile. Until they don't.