If there's demand, won't there be supply eventually?
If people will start paying premium for reasonable size flats while leaving some smaller units unoccupied, market will surely correct itself. It's true that for some time market might be skewed toward wrong sizes, but you don't have to ban anything outright to prevent it, some soft regulations might be sufficient.
These are buildings we're talking about. A city can get stuck with the wrong size units for a very long time. There's a reason things like the Parker-Morris space standards were developed, and they recommended 30m^2 for single occupancy dwellings in the UK in 1961.
The 220ft^2 apartments are 20.5m^2, not very large at all. The really tiny ones have communal shared cooking areas, which have the potential to be a social problem.
I think people are terrified of some kind of Stand on Zanzibar future where they're economically constrained into smaller and smaller spaces, and this is one way to push back.
In a neighborhood like mine (75% SFR, 25% MFR free-standing homes in West Cambridge), you can bet that I'll object to zoning changes that would allow "just building up". I don't need the noise, traffic, additional pressures on the school system, nor do I want to live in a mid-rise and high-rise district. If I did, I'd have bought in one...
There should be other options than building in your backyard. Find underused places and build up there. The biggest problem is what to build and how: it's amazingly easy to screw this one up (too sparse? too dense? too high? too low?)
You can't simply conclude it's one xor the other.
And roommates can pretty much always outbid families for housing.
The problem you run into is that even people who have the money, can't find anything to buy or rent, and zoning laws or other types of limitations, prevent fixing the problem by increasing supply.
When the real solution to this problem, as to many others, is increasing supply.
And of course, nothing about that project is "exponential".