No different, IMO. I live in a typical suburb - 4 bedroom homes, quarter acre lots. I don't want my neighbor running a B&B.

Is there room for compromise? Maybe. On general principle, I wouldn't mind my neighbor renting his house for a few weeks while he's on vacation. But, if the renter isn't a good guest (noisy). Or, instead of one renter for the duration, it's a new guest each night, I probably have a problem. Until AirBnB can convince me nothing like that will happen, I'd just as soon keep the rules as they are.

You're still skirting hotel regulations and occupancy taxes. There's a difference between, "My friend's coming to stay for awhile," and "$100/night to stay at Chateau d'Moi!"

In Manhattan?

Yes. In fact, one listed on airbnb. https://www.airbnb.com/rooms/62891

"The interior space is one small room, furnished with a loft bed, kitchenette and separate, full bathroom. "

They exist. Just very expensive.

as far as I know, there is only ONE free-standing house in Manhattan, and it is currently on the market for $13m - http://www.corcoran.com/nyc/Listings/Display/877330

There's a bunch of free-standing houses scattered through Inwood and Marble Hill. Not that they're a large portion of Manhattan's housing stock, and they're certainly not central, but they're there.

That listing's claiming to be the only free-standing mansion - which sounds a bit arbitrary to me.