1. There's regulation preventing landlords from raising rents too fast; often capping it at a much slower rate than the market itself is increasing
2. Once a tenant leaves, the landlord is free to increase the rent a lot more to catch up with the market
3. Therefore, if someone is Airbnb-ing an apartment they have lease on and living somewhere else, this decreases supply and causes other apartments to go up more in step (2) to make up for it
Maybe this is wrong? If so, can someone correct me?
Your understanding is incorrect. This only applies to rent controlled, and rent stabilized apartments. Most NYC apartments are neither of these, and rent stabilized itself has ceased to be effective in many cases.
The scenario you're describing is possible, kind of, maybe. Usually rent controlled apartments also have pretty strict laws about subletting, to prevent this exact kind of thing (and this is all legislation that predates airbnb).
1. There's regulation preventing landlords from raising rents too fast; often capping it at a much slower rate than the market itself is increasing
2. Once a tenant leaves, the landlord is free to increase the rent a lot more to catch up with the market
3. Therefore, if someone is Airbnb-ing an apartment they have lease on and living somewhere else, this decreases supply and causes other apartments to go up more in step (2) to make up for it
Maybe this is wrong? If so, can someone correct me?