Local housing has an artificially limited supply, actually. There's an absolute limit on housing per unit of area, but we get nowhere close to approaching that limit anywhere in the US. The real issue is zoning laws prohibiting building of new housing or favoring single family homes over apartment buildings creating markets where supply doesn't increase. If you address this and allow for building of higher density housing, prices will decrease and services like AirBNB stop being as big of an issue.
It doesn't help that local government politicians are frequently homeowners (and their constituents as well) that have a vested interest in keeping housing prices high. AirBNBs, apartment buildings, and high rises are going to negatively impact the value of their properties.