To actually resolve the housing crisis, you need there to be sufficient profit potential that private landlords are incentivized to build more housing. Rent control forbids this. Limits on rent increases, however, don't, really. Building a new apartment complex usually takes 3-4 years from permitting to completion to move-in. If rent increases are capped at 7% annually, then by the time your new project is ready for move-in, you can count on rents having gone up by 30-40%, assuming that that's where the market-clearing price would be. And if they haven't, they'll be higher the next year, and so on, until they equilibrate.

The idea behind caps on rent increases is to slow the bleeding and minimize disruption to families - having your rent go up 7% for 5 years is a lot less of a problem than having it go up 35% in one year and getting a month to decide whether to renew your lease, because it gives you time to look for alternatives and figure out what else in your life needs to change to make the numbers work.