A lot of times the "care" people get is really crappy also, in spite of expensive insurance. Oh, but they'll be sure to offer you a $30 orange juice. Then you'll be getting bills for months/years afterwords and not be completely sure what they are for.
I realize medicine is a specialty. I realize it takes a lot of training to be a doctor. But I've always believed that a lot of what medicine solves isn't unknowably esoteric. A lot of it can be solved by a person with some hands on experience and good observational powers and base knowledge (not brain surgery obviously but things like yeast infections, simple broken bones, etc.).
The whole thing really is more ripe for disruption than any other area I can think of.