I know they're already starting to re-enter the market in Dublin, where I'm currently in contact with people about housing as I'm looking at moving for school, and I don't think the populace would easily give those back up to let tourists come run them out of their town and Jack up prices again.
This assumes people value having greater supply of housing, and low housing costs. If this were true, wouldn't they just support building more housing generally? Yet almost every city tends to oppose building lots of new housing.
It seems like it could easily go in exactly the opposite direction. People seeing how hard the local economy has been hit, and wanting the tourism to pick back up at any cost. Homeowners see their property values have fallen, and want to reduce the housing supply to make them go back up. Of course, many people don't even believe in basic supply and demand at all when it comes to housing, so even this level of analysis may be applying too much logic to how the average person will react.
I’m not sure most people (or most cities) are saying they want a greater supply of housing. I suspect most people want to keep the character of a city and keep prices reasonable by mitigating against vampiric tendencies of some landowners/horders.
So ironically it could bring AirBnb back to their roots which is grow with unused and extra rooms by individual homeowners/renters.