Therein lies the problem. Rent control is not the only way to make housing affordable to low-income people. It's not the most efficient or effective way, either.
But it persists, because politically it's an easy concept (even if it's an ineffective one), and it also creates a stable voting bloc that will protect it, even if they don't actually need the rent control[0].
[0] In most places, rent control isn't means-tested, so you can end up with incredibly wealthy people living in very valuable properties for next to nothing. Ed Koch, the former mayor of NYC with a net worth of about $10 million, died living in a multimillion dollar penthouse apartment that he rented for $300/month, because the apartment was subject to rent control.