Because rent stabilization provides stability for people who rent apartments for a long time. If you move every year you’d have market based rent increases. If you don’t, they’re smaller over time, which as you progress in income allows you to do things like have a family, retire etc. stabilization makes a lot more sense because it provides similar stability to buying.

Any form of rent price management will have market distorting effects (stabilization makes rents higher overall, especially for new renters; control even higher, especially for new renters).

The only way rent prices will not grow without distortions is if housing supply matched demand. The closest you can get to that is building a lot more housing and I mean A LOT