There are many ways! The ones used by myself, my friends, and my family when moving to The Big City and looking for a job/permanent housing included:
1. Couch surfing with friends/family.
2. Youth hostels / YMCA.
3. Renting a terrible apartment cheap, sight-unseen,
breaking the lease early when better options became
available.
4. The Daughters of Divine Charity, et al, run boarding
houses.
5. Rent a place in the outer boroughs, Jersey, Yonkers,
etc, take the train in until you find something
closer.
6. Walk around until you see "room for rent" signs.
7. Check papers, Craiglist for roommates (*actual* room
sharing -- a number of people I know started off
renting a *bed*, not even a bed*room*.)
Ok, I wasn't being entirely literal. The point is AirBnB was just about the only way to find safe, convenient, relatively affordable housing for a few weeks. And it's probably going to get worse now given that this legislation applies to services like Craigslist as well.
AirBNB units make up 1/5 of 1% of the NYC's rental units. A bottleneck? no, but sizable and impactful, especially when you consider that these tend to be clustered around where they're convenient.
Convenient is not the right description -- high demand is. Who's to say an AirBnB is a worse use of space for, say, a unit in SoHo than a year-round resident?
AirBnB has real issues -- zoning, hotel tax, safety, etc -- but politicians like to use rent cost/resident displacement because it's an easy rallying call.
Eh, I don't know that most of the people I knew who sublet half a bedroom would ask themselves that question.
Subletting half a bedroom from a total stranger can be inconvenient and occasionally weird but if you're fresh out of college it's not really that different from the dorm room experience for most people. And it usually costs less than half what an apartment does a month, and is usually month to month or so.