If you look at the list of services, it's basically a list that does not include any service that requires an appointment. My company does scheduling for small businesses and, in industries like auto, there's just a maximum number of appointments each day that we're allowed to book.
It looks like Amazon punted on the hard part by constraining the availability to only specific services.
How does Amazon determine a company's availability when a customer books a job?
Most of these business I'd guess are probably in the 1-10 people range and probably not the most tech savvy. I can't imagine an adequate solution unless Amazon provides scheduling software and enforces adoption.