It seems to work alright to me.
We'll see where this takes us, but obviously if the population is dropping by 20% a year, keeping the theoretical option to charge a rent of 4k when the actual value is 2k won't matter.
Also, I'd like to add that landlords are incentivized to charge high rents anyway. Even without rent control there's not going to be $800 rents in San Francisco anytime soon, sorry.
This is just a holding pattern, right now. There's a slim chance that things could go back to normal, say with a quickly developed vaccine through decisive national leadership, and a lot of luck. In that case, those prices will look sensible again.
I think the odds of that are extremely low... but they're not 0%.
Probably, though, prices are going to crash. Some landlords will accept the inevitable and start charging less to rent out their rooms; if things are really caving in as people expect, landlords may be reluctant, but if it's that or lose money on empty rooms, they'll lower prices. And if things get that bad, then landlords will be lowering prices.
Think of all the AirBnB hosts making 0$, all the landlords with mortgages depending on some kind of rent to meet their bills. They'll lead the way, and others will follow, just to keep up.