One problem that can't probably solved by simply "focusing on the UX and better service" is that the service provider (medical professional) is both responsible for evaluating what's wrong with you (and what services you need) and the administering the treatment.

Judging the quality of the medical service is also often difficult. The true quality and the utility of the service you receive will often be apparent only years or decades later. Did a patient need for antibiotics for a basic viral infection? Probably not but it feels like a better service.