The gap between an enquiry and a first appointment
Almost every clinic and hospital is competent once a person is inside the building. The losses happen earlier, in the days between somebody deciding they need help and actually sitting in front of a clinician. Someone rings on a Saturday, the line is busy, they leave a message, nobody calls back until Tuesday, and by then they have gone somewhere closer.
That gap is an operational problem rather than a marketing one, and it is fixed with ordinary things: one queue instead of four, an owner for every enquiry, a response clock, and a follow-up that is easy to reply to. The only unusual constraint in healthcare is that all of this must be done discreetly, which shapes almost every design decision that follows.