"their role in giving birth [...] is rarely even noted in passing in traditional music"

Could this be because there was no point in writing songs about it? It was, and is, part of everyday life - immensely important but not actually newsworthy, not a thing to memorialise. All the recognition necessary will be found wherever there is a happy family.

I've always been curious that another subject almost absent from traditional songs is success in business or politics. Plenty about unjust laws and downtrodden labourers, occasional mention of returning with gold in great store, just one (Byker Hill) about a worker doing well from his job. Perhaps successful businessmen & politicians didn't need to write songs - they just carried on doing what they were good at.