Capitalism != Anarchy. Free markets still require laws addressing theft, property ownership, contract law, etc. Protectionism, however, simply rewards first comers. Disruption is the crux of a free market and should be embraced not lobbied against. Services that people dislike the most due to cost or service rendered (airlines, health insurance, telecom providers) are often the most regulated.
It's funny you say that, because one of the features of AirBnB is that it has "disrupted" property ownership and contract law. A huge number of AirBnB properties are being sublet in direct violation of the terms of the tenancy that the tenant agreed with the landlord.
If you want a state that strictly enforces contracts between parties and property ownership rights then that's a state where AirBnB wouldn't exist.
To the extent that AirBnB hosts are violating their contract with the landlord, the state should be involved to enforce that. However if the host owns the property (or has contract permission to sublet) the state should not be involved. The state may also get involved is someone (guest or legitimate owner) is affecting their neighbors (excessive noise for example).
I can recognize that some AirBnB's are not legal even while arguing that as a whole the idea should be legal.
I think the legality of operating an AirBNB out of a residence that you own depends on the zoning ordinances that the property is in. (Renting out your farmhouse is probably ok; renting out your suburban or urban house or condo as a business proposition probably violates zoning ordinances and would require requesting a variance from your local governing council with appropriate public hearings and notifications to your neighbors.)
You are correct, but I disagree with those zoning rules in general. Specific zoning rules that prevent behavior that is significantly negative to the neighbors I'll allow, but most zoning is about keeping some other class (generally blacks or poor) out.
A tenant subletting their apartment against the terms of their contract is obviously an issue and should be addressed between the actual property owner and the current lessee. However, lobbying for a blanket law against subletting if the actual property owner is OK with it is where protectionism comes into play.