NYC apartments are tiny because NYC just doesn't have enough housing in general, so everything that's allowed to be subdivided gets subdivided (and some things that aren't allowed get subdivided too).
Partly, but also smaller living space is in fact part of the tradeoff that you make when building stuff close together. It's a worthwhile tradeoff in my opinion, but I'm also not saying that single-family car-centric suburbs should be illegal for people who prefer it, unlike how building denser housing is illegal in many expensive cities.
While that's true, there's a significant difference between "you can't give everybody a McMansion" and "everybody must live in spaces objectively describable as 'tiny'". My objection is to the latter.
When I first played Sim City I imagined a future of towering soundproofed arcologies where everyone still had a private yard on a giant balcony, so you could increase density without overly decreasing living space per household. Is anyone trying to build like that?