Parents can be the customer. Often they are, sometimes they aren't. Sometimes government is the customer. For some interventions, like public health education or vaccination campaigns, government is the only customer. Or perhaps a volunteer clinic. Or a concerned neighbor. Or...

In none of these cases is the baby the customer, which is my point: market mechanisms alone don't solve all problems. Which is why we have things like "parental love" and "public service". Markets are tools, not magic unicorns.