I'm in San Francisco, the home of airbnb and a hotbed for this very battle.
https://www.airbnb.com/rooms/350391
The airbnb software DOES include a field for hosts (here in San Francisco) to enter our STR (Short Term Rental) registratrion #. I'm one of the minority of SF hosts who is fully registered and filing my quarterly reports to the city. But my STR number does not show on some of airbnbs many software permutations. It show up on the web site but on the android app and ipad app all you see is (PHONE NUMBER HIDDEN) where the number is supposed to display (under 'Other Things to Note' section, at the absolute bottom of your listing description).