The last time I was in NYC was 10+ years ago, but from what I recall, operating the turnstiles correctly required some experience: you need to know that they require manual operation (not obvious to first-time users), and then you also have to operate them at the correct speed (going too fast doesn’t let you through).

Systems with fare gates (i.e. most systems worldwide) don’t have these problems, because it’s obvious when you can pass through.

Then factor in lots of tourists/visitors (who aren’t used to this system) + aforementioned small stations.