The US does not limit the number of doctors that can graduate. The limit is on the number of residencies funded by medicare. If the private sector wanted more doctors in order to pay doctors less, they could just offer paid residencies themselves. Somehow the free market hasn't solved that one. This ignores that doctors' salaries aren't a significant cause of the problems and insurance companies are the true root of high prices.

Rent control stabilizes prices while more supply can be built, because it is in the interests of society for people to be able to afford to live, and we can't will additional buildings into place overnight. High eviction rates destroy communities and have many negative side effects.

In the absence of regulation, corporations lie, cheat, and steal, and have a massive power imbalance against ordinary people. No one has enough time and energy to research every option for everything in their daily life, and they rely on laws to establish safety measures they can rely on.