The problem isn't really rent control. Same with criminal checks and credit checks. The problem is with an eviction process that in owner occupied properties should be instantaneous, like a hotel eviction, and within days for nonpayment or for damage in other cases. Paying people to leave or relocation costs also need to be thrown out.
The rental market will then sort itself out.
Small landlords (<four units) need to be able to get much larger deposits, say up to ten times the monthly rent.
Many houses sit empty that would be rented if proper security was provided.