> stay in hotels instead of buying second homes, the net effect should be to increase the cost of hotel rooms and reduce the cost of owned-housing.

airbnb begs to differ?

the conversion goes from owned/rented housing to airbnb conversions

however, the slack is absorbed, and the airbnbs are gonna about match the actual need for how many ultra-rich people are actually in NY at a time

Good news, Airbnb can't operate in NYC.

Here in Chicago, they're banned from certain wards

Not in NYC. Airbnb is effectively outlawed by regulation there.