I agree with your concerns, but why not just distinguish between personal/regular/single user and power/multi-listing/comercial users? Craigslist does this pretty well with their "for sale by owner" vs. "for sale by dealer" option.
Good, bad, or otherwise, the owner/dealer distinction clarifies this. Eventually the site simply becomes one-stop shopping for atty's g'l intent on enforcement.
Does Craigslist investigate every item sold to make sure it's not stolen?
No, but they probably should. Pawnshops, in many jurisdictions at least, are supposed to hold things that they buy in case they turn out to be stolen. You can be on the hook for fencing something even if you didn't know it was stolen.
How large should my obligation be, to make sure you aren't breaking the law?
If you think there's a Craigslist seller selling illegal goods, arrest them. Nice and easy.
If you think someone's violating the terms of their lease, tell their landlord.
The system's far less than perfect, but it does exist and is explicitly supported.
Craigslist does have terms of service, and relies on a user-based flagging method to remove nonconforming content. They claim significant deletions base on this, though my own experience is of massive levels of bad-actor behavior, less of illegal activity and more of rampant spam posting in several sale-by-dealer categories, many lasting for years. Large consequence is that those sections of Craigslist are of exceptionally little value to me. Actually, much of CL doesn't really do much for me these days....
But despite that: the overwhelming majority of activity on CL is at least reasonably above-board.
In the case of AirBnB, the article here notes that 40% of rental volume is from multi-listing members. That is, people not leasing single rooms or properties, but managing multiple properties. Which further discounts professionals who only manage a single property.
That is: a large and visible chunk of AirBnB is not the "come stay at our house" vision the company's propaganda promotes, but is a commercial rentals service not meeting standards of either housing or hotel accomodations.