AirBnB / couch surfing style sites are likely to work better for people with somewhat flexible schedules that can accommodate potentially being stranded and having to find a hotel at the last minute. In exchange for a small risk you meet local people in an informal way that you just can't get if you stay in a hotel.
I'm not even remotely interested in meeting the typical person who wants to let out a room, but I'm happy to pay a decent premium over a midrange hotel to get an apartment instead of a hotel room, and have been happy every time I've done that.
If you're going somewhere regularly you can try a place once and then decide whether you want to stay there more often. There are some nice apartments as you say.
There is a weird sweet spot for AirBnB rental timing. If it's too far in advance the person doesn't know if they are going to be around to give you keys, or gone so that you can stay there. If it's too soon they won't have time to straighten up. I'm guessing the best luck happens around 4 days in advance, with a spot that looks like a reposted vrbo listing. (I.e. a semi-pro)
Also I think sometime in may short term AirBnB listings are effectively banned in NYC.
I reallllly want this service to work. But the concept is already so intrinsically out of my comfort zone that it doesn't take much of a nudge to send me back to super-pricey VRBO.