The solution is to ban short term leasing in cities, increase taxes on sales of property within a certain timeframe and increase taxes on owners who have a property with nobody registered to live in it.
Basically you don't want people buying property to flip it quickly, to hoard it or to have a holiday home. You only want buyers who'll live in the property and/or rent it long term.
High end estimates of AirBnB apartments are about 4% of units in the most popular neighborhoods -- Times Square, the East Village, Williamsburg. Drift out to Park Slope and you can see 2%, maybe.
House hoarding? Very few people pay a mortgage for empty space when they can get a tenant to pay the mortgage instead. The real house hoarding is the high end luxury market with $20 million penthouses, where renters were never in the picture.
We don't need to free up 4-5% more units in the most popular neighborhoods. It'll help a little, yes? It's just that it's such pathetically small thinking.
Why don't we have a plan to build 50% more units citywide, and make housing actually affordable? Hell, it's New York. Build us 100% more apartments. Put real price reductions on the table. Do what it takes to chop rental prices in half.
Land, on the other hand, is severely underused. Zoning changes could easily triple the housing supply in American cities. That's a lot better than 5-10%.