That system is ripe for abuse as well. You would have to outlaw a landlord from being to ask what their financial status is, doing credit checks, proof of employment. Otherwise homes for the homeless will have rents with disproportionate high rents for poor quality slum homes.
Also without rent control, you will suddenly find cities suddenly very empty of people able to do things like get you your coffee. And shipping them in every day from 100 miles away is a dystopian nightmare.
No... that's not really the effect of no rent control. In fact rent control is often the cause of excessive credit checks, proof of employment, etc. Maybe in the short run no rent control would make disproportionate high rents, but not in the long run. In fact it's the opposite. No rent control results in something like Hong Kong: abundant, extremely tiny apartments that people can afford. That may not be ideal, but it's certainly better than being homeless.
Luxury apartments are lucrative, sure, but if you can fit more rooms into a given space you can often make even more money. For example if you could have 1 apartment and charge $3000, or 2 apartments and charge $1700, the 2 apartments are a better deal.
The above plan will have the effect of landlords knowing how much those only on the minimum living allowance can pay. Combine that with the ability to still perform credit checks and it's ripe for abuse. If you have a guaranteed minimum income that is suffcient to qualify you for the apartment, you should probably be able to skip the credit check for it.
Citing Hong Kong struck me as odd. It's probably better being homeless in certain states. I think most people have seen the following, or similar, set of pictures about Hong Kong micro-apartments:
Real urban planning has low income housing distributed throughout the city. If not, the wage slaves have to be shipped in. Some form of rent control/social housing incentives have to be in place. Otherwise you get situations in the states where welfare mothers have to bus 3 hours each way to get to their minimum wage job.
Also without rent control, you will suddenly find cities suddenly very empty of people able to do things like get you your coffee. And shipping them in every day from 100 miles away is a dystopian nightmare.