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.
It may increase overall life quality and reduce number of appeals to GP
Another idea was, that often when I slightly sick, it's unclear whether I need some medical help or just some advice is fine, or may be I can just lay in the bed for a day or two. It may reduce number of irrelevant calls to GP
To your point about supply, is it fine to have telemedicine calls with doctors from other countries? Not sure about prescriptions though.. also it may make medical help less available in countries with lower salaries than in US for example What's your thoughts?
As for daily health monitoring etc, I think that's a crowded space that's already in vogue right now - think Apple watch's features which remind you to stand for a minute every hour and encourage you to exercise by gamifying it. That doesn't mean you can't do anything new - just, IMO, not the most "high impact" it can be, especially when "low hanging fruit" like mental health are very, very crowded.
I think in general healthcare is a very difficult field to take on unless you have a lot of resources and are willing to work with the law (for good reason, ofc.) That doesn't mean you shouldn't try it, just that you might find something else that is higher impact and less likely to frustrate or burn you out.