They should be requiring that Airbnb help them enforce it. Airbnb could easily require you to input a permit number when you create a listing then keep track of the number of days you are renting without a host present in order to make sure you don't go over it. They should also be reporting your rental income to the state for tax purposes.
See, this is the part that truly makes me ill. I don't want the government, at any level, to outsource its habituation. Regulations are one thing - on the local level they're usually tolerable - but bureaucratic integration is another.
In the anarcho-capitalist community we call it slave labor. It is a bit of a stretch to say as much, but it get's clumped under the same umbrella as conscription. i.e. Government compelling you to do labor (usually for free), which is just a bit away from "government compelling you to enforce it's laws/regulation/process/bureaucracy/tax enforcement on it's behalf, at your own personal business cost". Assuming that's what you mean with bureaucratic integration? i.e. Government getting businesses to help them enforce their bureaucracy.
I don't think "a bit of a stretch" quite captures the exaggeration. It is, in fact, a huge ridiculous stretch that should offend anyone who knows what slavery actually is. It's not even in the same ballpark as conscription. (I recognize, though, that you appear not to entirely buy this terminology yourself, which is admirable. The anarcho-capitalist community could use a few more people who think critically and take language seriously.)
In cases like this the government does not compel anyone to do anything. Rather, it permits them to engage in a particular line of business on the condition that it does so in a way that attempts to re-internalize what would otherwise be a host of harmful externalities.
