I think this is similar to being charged for a service prior to the service. Seems to be the norm now? My mom had an epidural earlier this year and she was required to pay her portion up front. I thought it was crazy! Then a few months later I get a bill for my baby that I have yet to deliver. That's when I realized this is the new norm.
I still haven't paid it. I think it's really silly to charge for something that can have SO many variables. What are they going to do, push the baby back in if I haven't paid? I just hate how our insurance has declined in the last several years (and by our, I mean my family's). I didn't get one bill for either of my sons nearly 9 and 7 years ago (except for the voluntary procedure for boys). Premiums are higher, deductibles are outrageous and now they want prepayment for something that can vary by several thousands of dollars! In fact, they sent me the bill while I was still in the first trimester in which there's so much uncertainty at that point!
So while I've never been asked to leave a credit card, I've been asked to prepay!