Actually, the AnCap answer and the AnCap solution are not the same. The answer can vary however much you want, but the solution is pretty clear: People only get their kids circumcised because it's included in the hospital bill. Circumcisions cost money. Think about it, even if hospitals are cheaper (they would be, and insurance companies would mainly be for travel rather than everyday costs), on top of the medical bill what unnecessary costs are you adding by getting your kid circumcised when you pay the bill out-of-pocket? Assuming you don't botch the procedure as a parent, you're paying for…
>Anesthetics
>A medically unnecessary procedure
>Followup doctor visits to make sure your kid's dick doesn't get infected/he doesn't bleed to death
>Room in the hospital to perform the procedure
>Likely extra time for the mother in the hospital before release with the baby
>etc.
Even assuming you could find some rabbi who would do it for free, the hospital most certainly isn't going to let him perform the surgery on their dime, so after the first couple deaths from a botched surgery and the ensuing media outcry since it wouldn't be funded by insurance/the government/etc. you'd probably end up with circumcision being a very Jewish problem that doesn't affect anyone else. You can't remove all evil from the world, but you can sure as hell let the market remove most of it.