Obviously it would be expensive, but surely better than not having it? I can imagine all sorts of scenarios where it would be vital.
I'm looking at going to my 12 week scan alone, and as I've had hardly any symptoms this pregnancy compared to previous I'm worried it might be an MMC, so would prefer DH to be there. But DH will have to take the day off work to look after DC. DC can't come into scan with us. The hospital is over two hours drive, so a round trip of about six hours (they are always running late IME) which is far too much childcare to ask of a friend etc. My MIL does do regular childcare and could normally help but she's sprained her ankle badly and can't at the moment. There's no ad hoc childcare available locally to where we live. I'm lucky that DH actually exists and can take the day off, otherwise I just wouldn't be getting a scan at all!
Just one example, but in my situation I'd be prepared to pay quite a lot for one off childcare for hospital appointments. Ditto if I went into labour early and hadn't sorted anyone to look after DC. Or if there was an accident. Etc etc.
I'm sure there's a good reason nobody thinks it's worth running this service, but what is it? Curious!