It's funny... I realize I have no precise idea.
A factor is that, as age increases, one sees physicians less often. Maybe one gets fewer illnesses through schoolmates, maybe one gets immunized, maybe parents freak out less.
Furthermore, there is "exam" and "exam". If I come to the doctor for a severe throat ache, he or she will look at my throat, maybe listen to my lungs. This is not embarrassing, it's not like disrobing into underwear or worse.
I recall, as a teenager, going to the doctor with a cheque from my mother for payment.