Rent didn’t shoot up, how could it, the whole point of the law was it was frozen.
I think you’re missing the forest for the trees in this entire conversation: rent has been skyrocketing everywhere, in every G8 country, for the last 20 years. Especially in places like London, NYC, LA, Seattle, Paris, Toronto, Bay Area, etc. Hell, even in Salt Lake City where I used to live my rent went from £1816/mon to £2600/mon for the same flat, in just 2 years. And none of those cities have classic rent control (NYC has a few places which have it, but overall it doesn’t). So clearly with a free market, pure capitalist approach, rents have only been skyrocketing. Same thing for housing to buy, have you tried buying a house lately?
So to claim that rent control or rent freezes lead to higher rentals or less supply is wrong, because rents are going up in a free market too, and supply is already at an all time low (hence the prices shooting up).
So you’re fucked in either situation. The real problem is there just isn’t enough supply of shelter for people, and that’s because if you leave it to the free market, there’s no incentive to build affordable housing with no profit. Hence, because shelter is something required by citizens, government should be building it even at a huge loss. Just like government provides fire brigade and military at a financial loss, because people need these things. You don’t leave essential services to the private market because it may not be profitable to do them, for example, rural communities have shite internet, why? because it’s not profitable to dig and lay fibre optic cable into some rural hinterland for just a few hundred customers. So in Norway, the government steps in lays that fiber optic at a financial loss because it wants its citizens to have a better life. Same for housing. If the private sector isn’t doing it, the government should be. Just like in the 60s.