New York's rent stabilization isn't that bad, but it also doesn't have a major effect on rents, either for those who have it or those who don't. (Rent-stabilized apartments can go up by a few percent per year.) It's the 1947-era legacy rent
control that is patently ridiculous.
Most people underestimate the harm of that program because they don't understand price elasticity. It's true that only ~1-2% of apartments are under that system. However, 1-2% supply destruction can actually double prices. (See: oil shocks.)
Another problem is that this country is run by scumbags and pussies who allow foreigners to own real estate (many countries don't). Now, I'm all for a reasonably open immigration policy, and letting foreigners live here is not the issue. (The people who move here to live here don't have a major effect on the rent, and are good for the country overall.) But the types of foreigners who buy U.S. real estate are usually corrupt officials who want a place to live if their own country brings them to trial. (In China, corruption is a death-penalty offense.) This is the real reason why Silicon Valley is so expensive: every fucking Communist Party scumbag in China and murdering Russian oligarch and Arab slave state billionaire has bought a place (even if it goes uninhabited) in California. It doesn't affect a large number of houses, strictly speaking, but it's enough of a margin to have massive impacts on the price level.
I am amazed at Americans' willingness to be "patriotic" about stupid things and get into nonsensical wars... but then we go and let corrupt, murdering dictators and billionaires from all over the world buy California and Manhattan real estate. It's fucking disgusting.