Of course, nobody says your technical solution has to be about increasing the number of doctors - access to healthcare can be improved by, say, helping doctors examine or treat more patients than before by automating the mundane stuff, or even some sort of miracle tech that can take care of the most common illnesses without any doctor's intervention (I'm skeptical that this would be possible without AGI).
It's definitely not the kind of thing you can fix in a solo team part time, though.