The problem with charging below market prices for anything is that it necessarily leads to a mismatch of supply and demand. So the question is how do you allocate that supply?

One way is to have hidden costs. This could range from straight up bribes, to paid consultants to fill out a lot of forms or talk to the right people, to just knowing someone

Another way is a lottery which benefits a tiny percentage of people. Sure it's "fair" but the incentive to rig it is huge

But even with a lottery it's still inefficient. If you give someone an apartment with a market rent of 4k for only 1k you're effectively giving them a 3k apartment subsidy. But if you handed them 3k, maybe they would spend 1k dollars on extra apartment and 2k for something else.

There are other distortions. Overall these are the worst kinds of policies because it's all hidden costs. If we realized that with a system like this we're giving 1 out of 1k eligible people the equivalent of a 30k a year transfer, we'd likely realize it's a ridiculous policy. But instead we just say how nice it is so and so is paying only 600 Euros to live in the center of Paris