Nobody is saying "just buy a house," because everybody is complaining about how the lack of housing is a major part of the issue. Apart from what you said on imposing limits and increasing protections for renters, the other main issue is to diverge equity from housing. Having the main way to accrue wealth be tied to the basic necessity of having a roof over your head puts a major incentive on people and corporations to buy up property. Housing becomes an investment at that point, not a service. There are people and companies sitting on empty houses because driving up the market by removing inventory is a more profitable investment than actually renting them out.

And if there were more options besides single family housing, people wouldn't be forced to buy a house every time they moved as well. The US especially is really bad at this. We have high density apartments and condos, and single family homes, but a major lack of medium density housing. If we had more multi-family homes, duplexes, town houses, and smaller scale apartment and condo buildings, this would be a lot less of an issue. With more variety in housing types, the demand for single family homes would be a lot less and would help to reduce housing prices and make things more affordable for those who do want to buy a house.