I agree with you that I think we need to be careful about asking corporations to be legislative authorities. I'd say this is very similar to the Backpage scandal in which employees were beyond reasonably turning a blind eye to very illegal, preventable behavior happening on their platform. Why not just allow people to involve the authorities in that situation as well?
What I'm proposing seems extremely reasonable considering AirBnB is, at least in NYC and other major metro areas, primarily used for breaking the law.
Here's the thing I think most people are missing: almost every state, city, municipality etc. in existing has laws against short term rentals. The reason for this is very clear because the issues have already been considered at the civic level. There's no reason to think that just because a platform emerged that makes this illegal behavior easier that the behavior has changed. Zoning exists for a reason. People don't want short term rentals. As far as I can tell the vast majority of AirBnB's business is illegal.
This is different from YouTube in that there is a very large legitimate use for YouTube. There is a legitimate use for AirBnB, it's just not $38B large. Asking them to make enforcement easier for externalities seems like a very reasonable alternative to heavy handed government regulation (ie: requiring short term rentals to be registered with cities, which is what cities are doing now to respond to AirBnB's lack of self-policing).