I'm sure you have proctologists! You must, for all the prostate problems!
But yeah, in Canada, anyway, we're a lot less GP-focussed. You normally have a pediatrician for your children, much as you normally have an obstetrician for your pregnancy.
I do prefer the English way.
And I stand corrected re: sciatica.
The French are weird about medical stuff, aren't they, between crise de foie type stuff. And they treat babies for snuffly colds.