No. Only few cities have agreements with Airbnb like you describe.
The default (which applies to 99% of the hosts) ist that Airbnb does not collect taxes and pay them to your city/country for you.
Anyhow its wrong to ask a city to make particular agreements with Airbnb, Wimdo or whoever comes next. There are laws, which regulate rentals, and they should be obeyed - by the hosts as well as by Airbnb.
Airbnb should not accept hosts, which do not have a license - it's as simple as that. But then Airbnb would have the burden to check the legality (and even the existence!) of their hosts, which means on site labour. But Airbnb lives from the fact, that there are fake properties, and therefore Airbnb urges guests to pay through them as an escrow service. Airbnb pretends to be liable for problems which wouldn't exist, if there wasn't Airbnb. Believe me: my family rented apartments for several decades without any problems and without paying commissions to any agency. Now with Airbnb the unfair competition grows exponetially and problems arise which never happened before. And for that disservice we should pay 18% to Airbnb?!?