This is not the intended use of the book a pro scheduler. If you're not wanting players to book on their own, I would recommend creating a page like this customer did to showcase a pro and instructions on how to book with this pro.

Hi Alex- please reach out to our Customer Success team. If a membership expires due to an end date, there should be an auto-reassignment picking up. Our team reviewed and we did make an update around this during the spring. We'd like our CS team to take a deeper look at this and tag as a bug if it's not working as expected. 

We recommend adding a reservation disclosure (Portal Settings > Reservation Disclosure) so the Terms and Conditions can be viewed prior to payment. If a disclosure is used, this extra link will pop up below the payment where the customer can view the disclosure, and by proceeding they're agreeing to the disclosure policy.