Airbnb doesn't help with tenants who wont' leave. Just like Craigslist doesn't help with tenants who dont' leave, if you use Craigslist to get a renter. Hosts have to take on these risks -- I agree with you though that having to go through a 6 month process just to get someone out of your home who has overstayed their reservation, is not acceptable. This is a serious problem in many states and I believe laws need to be changed, because one should not have to go to court to get someone out of one's home.
However, the laws are not the same for short term rentals as they are for long term rentals -- meaning, for short term rentals one doesn't usually have to go to court to get someone out. Otherwise hotels could not do business, if they had to file a lawsuit and wait 6 months to get someone out of their hotel room who refused to vacate, when another guest was due to arrive that afternoon, and then another the next week , and so on. Having to file lawsuits to evict overstaying hotel guests would very rapidly put any hotel out of business!!
See this info for instance
Evicting short term guests in California
on the laws pertaining to short term guests in California, which illustrates how the laws on short term guests are different than those for long term renters. IN California, if someone is a short term renter and does not leave on time, if you follow the procedure described in this document, you can simply remove the person's belongings from the room and lock them out of the room. THere is no need to go to court or file a suit. If they stay beyond check out time they are guilty of the misdemeanor crime of trespassing. This is true only for rentals less than 30 days long.
California also has a "single lodger" law which states that if you rent (for over 30 days) to only one renter in the home you live in, you can evict them without filing a lawsuit. You give them 30 days' notice (a fixed length rental includes an implicit 30 days' notice) and then if they dont' leave at that point, you can either lock them out or have the police remove them, as they are guilty of the crime of trespassing.
Info on SIngle Lodger Law in California