Affordable housing is something that would actually be solved by free markets. It's the heavily regulated (almost socialistic) systems when building new homes to new people in a growing city is not allowed (because the old residents don't want their city to grow), so supply is now allowed to meet the demand, when we have these problems.
Everything could be solved by a perfect free marker where everyone had perfect information, zero latency in decision making and where making a decision cost nothing. Trouble is, IRL, none of those assumptions is even remotely true. Just as the renter signs an agreement, so does the landlord; rent controls skew the bargain but they do it for both parties. If the landloard didn't want to have a rent-controlled tenant for 10 years, then they should have magically known (using their perfect market information, duh!) that that tenant would be there 10 years and rented to someone else who wouldn't.
A desirable city with very limited new construction will lead to increasing prices. You can use rent control to give cheaper housing to a smallish number of people, who kind of win in this lottery and get cheaper housing the others. But there will be those others, lots of them, who were not among the "lottery winners" and who will have to resort ti living with a much longer commute.
If demand is high, building new homes for people should be allowed.
