In application Toronto has seen the opposite effect to what you describe. We hear this argument over and over as we just had our rent control stripped, but it’s counter to the experience.

Here’s one write-up:

https://urbantoronto.ca/news/2018/11/people-why-universal-re...

Is that for rent control as in New York or San Francisco, where the allowed rent increases are very small; or for rent control as in San Jose (8% until reduced to 5% in 2016) or Oregon, or maybe this bill, where the allowed rent increase is larger than most of market increases?

A limit of 5% + inflation is probably more than most markets in most years, and more importantly, is a big enough limit that most leases will be able to catch up to the market over a few years.

So, this would still distort the rental market, but in a much more limited way, that may be more likely to actually help people.