Funny but I have come to regard the "effort and commitment" as part of the recovery mechanism. Causal or concomitant, I have no idea, let's just say 'linked'.
By the same token I have come to regard "convenience" as, if not a great evil, some kind of joker/trickster that lures us down a dark path.
And I don’t know what the statistics are, but a significant percentage of people with gym memberships rarely go to the gym. I suspect the percentage of people with free (i.e. payed for by insurance) insurance who rarely go would be much higher.
Maybe your doctor should even get a small reward each time you pass the basic health check, so that in aggregate they are better aligned with keeping people in shape for those checks.
Insurance likes low variance outcomes because they’re easier to model accurately
Because neither of those things are necessary to exercise.
I bet if you asked your GP for some body weight exercises you could do at home he'd happily provide some for you and insurance would cover the visit.