This is what happened in California. The statewide rent control is 5% plus inflation per year, capped at 10% per year. There’s a bunch of exclusions too, like the property has to be at least 15 years old, and single-family homes that aren’t owned by a corporation are excluded too. I think the builders and landlords had quite a bit of a say in it, hence the limit being so high above inflation (assuming inflation of <=5%).
Still a lot better than it used to be. It applies to month-to-month rentals too, so you can get the flexibility of a month-to-month rental while still having a limit on the rent increase per year. Evictions also need to have just cause and there’s a notice period of 60 days if the tenant has lived there for longer than a year.