In a rent-control environment, people have incentive to hoard their rent-controlled apartment as well, especially if rents reset on turnover. If I have a rent-controlled apartment that's well below its replacement cost to me, I'm going to be more inclined to keep it when I initially move in with a significant other. If that relationship fails, I can move back. If it were a market rate apartment, I'd have much less to almost no incentive to do that.
And when I was looking for a place, I came across a couple people playing landlord and trying to sublet out their rent controlled place for more than they were paying the landlord.
It’s pretty broken, at least in NYC.
And there are also people who would be interested in an apartment in a different city. A favorite vacation destination. Near the in-laws so you can visit and yet get away. A short term job. The foreigner in an unstable country who wants every possible reason for customs to let him in if things get bad enough to flee. Hotels fill some of that, but if the price was right an apartment where you can leave spare things instead of packing starts to look nice.
Mostly it isn't economical, and I don't see that changing. However in the imagined world where it was very cheap you might be interested in a second flat just across town. It would change your lifestyle to use it.