When I got my driver's license at age 17 (or possibly the learner's permit? I forget), we learned that the car insurance company would reduce the premium for me if we regularly submitted them some kind of proof that I was getting good grades. It's possible this was some kind of "public-service program to encourage desired behavior", but I suspect that at least part of why they did it was because straight-A students are less likely to get into accidents.

For medical insurance, it seems they could at least do something like "if you send us evidence of healthy exercise/diet/weight, then we'll lower your premiums; otherwise you'll get a premium based on the estimated risk of the set of people who don't do this". (If the government doesn't forbid it. healthcare.gov says "They also can’t take your current health or medical history into account", which sounds like it might rule out some of that.)