The measurable problem in a clinic is not usually booking, it is non-attendance and the phone line being occupied by people asking for a slot.
Online booking against real practitioner availability takes the routine bookings off the counter, and automated reminders by email or messaging reduce the number of empty slots. Schedule management stays with the clinic, including blocking out leave and adjusting session lengths per practitioner.
Patient information handling is kept deliberately minimal on the public side - the booking layer collects what is needed to hold an appointment and no more, with clinical records remaining in the practice's own system.