The more efficient these rentals are run, the higher the profit the government makes. The more money the government makes, the less they need to tax and the more services they can provide, and the more votes you get. If they don't run these well, people will leave to the private sector, reducing government income, which would then have to cut services and raise taxes, losing them votes. So there is a strong incentive to run the service efficiently.

Hmm, it seems like you're suggesting setting up a system where the private and public sectors keep the other in-check, with incentives to make sure it happens. But I see some practical points of concern, e.g. in most rent-controlled housing, the rent (eventually) gets to be much lower than the private market - thus removing pressure that customers will leave. Also, historically most governments seem to have no trouble getting votes even as their services become more and more inefficient over time. I guess I just don't see it working as you described. But its quite possible that I'm just too cynical! :)