You over analyze.
First thing you've said that I agree with.
In a society where it's normal not to analyze at all, any analysis at all is by normative standards over analysis.
You and your students represent a limited set. Membership to your set is restricted to people with certain views (and limits on their views), such as the view that getting a medical is no big deal, and the need to maintain a medical is no real risk. That means your group, by its nature, will exclude those with other views which may be common outside the set.
How many people never even picked up the phone to ask about lessons because those hoops exist? You don't know. However, talking to people outside the industry (this is where it helps to work in another field), you can get a baseline by doing things like telling people they should try flying. I've done that.
A surprising number of people, in my experience, cite the medical as a barrier. Not because they know they would fail, and not (when I probed) that it sounds like they would fail, but because it's an extra hassle. This is amongst people who ride motorcycles and do other relatively daring things for fun.
What percentage? I don't know. It's non-zero though. Add all the other perceived hoops and ready excuses and you have fewer students, GA has fewer pilots, than it should.