I live in a rented apartment so I can't legally host on Airbnb - but I'd love to simultaneously room-swap with people in other cities when I travel... (Eg swap my place in London with someone in Berlin for a week or two)
I don't think you can legally do that if you can't legally host in AirBnB. You may, but e.g. my lease (before I owned my apartment) specifically limited non-family[0] stays to no more than 1 week at a time, and no more than 4 weeks per year total. On one hand, it is non-trivially onerous. On the other hand, I really liked the apartment, and I understood the rationale.
[0] the "family" was very broadly defined - e.g it explicitly included unmarried S/O and their family, and implicitly close friends. but it wouldn't have included "someone I never met and who found me on couchsurfing.org".