One thing I thought from the show is Maki seemed to love song writing & not to want to go into her parents hospital - I'm not sure she would do it - or if she had any pressure to. Also her parents own it/run it right? If they wanted her to take over, wouldn't she be in management? A doctor isn't gonna know the first thing about running the place.
Remember that Maki's dad is a doctor himself. The way that doctoring works in Japan — or at least the way it works in fiction! — is that a wealthy doctor is wealthy by owning and running a hospital. There's therefore double pressure on their heirs: they must take over the family business, and to do that, they must be a doctor themselves. You get the impression that Japanese people wouldn't trust a hospital owned by, say, an MBA — and given how medicine (particularly the cost) has gone in the US in the few decades since hospitals became profit centers run by businesspeople, I can't blame them.
I assume that, because of this trend, either there are (possibly optional) classes in administration in Japanese med schools, or that the owner of a hospital or clinic is not the day-to-day manager. It's certainly true that any sizable hospital is going to have a good deal of administrative staff, and that that staff would not disappear when Maki takes over, so it's not like she'd go from, say, surgeon to the one who has to personally order bandage restocking and make sure the sheets are washed.