The markets with rent control have astronomical increases in rent when compared to markets without rent control. Also, you lose supply when there is a unit that it doesn't make sense to renovate because the future rent won't be high enough to cover it. So it remains unrented instead.
I mean, I would argue that's why rent control exists in the first place: Because there is a market with astronomical increases in rent (not the other way around, like you are suggesting)
