Hi Helen3,
I completely agree with you.
Please keep in mind though there are third agencies out there that are exclusive to travel nurses and they do do an excellent job. Most of those RN's work as much as possible. I know as I was one of those nurses and there are many travel nursing agencies out there. Google or better yet call you local hospital, ask for the staffing department and then ask them what is their preferred provider for contract nurses and call them directly. One good agency is tarvelnursehousing.com (they would give you a 3rd party app Keycheck to do a background check.
The reason I stayed with AirBnB is that the local hospital in town does not use a lot of travelers and they are far priced below what one can charge through AirBnB, more as if a tenant was living there.
I do suggest looking into it if interested. My biggest turn down was that I had a deal with guests directly, background check and all and it was too cumbersome for me. Sometimes some medical staffing companies do all for you as well. Research a little.
AirBnB is not set up in ways you are looking for though it is doable and highly rated way of running a STR as well.
Good luck!
Bettye6