Actually both my daughters were a month early. Not gonna lie: took some Fridays and 4pm exits now that I think about it to sit or help feed at the NICU but didn't straight-up disappear for four consecutive weeks. Even here the mommy is exponentially more important and "effective" than dad.
Now this was not ideal but plenty of preemies were in serious dire condition way beyond my early gals. In these very rare instances I'd expect any employer to do the right thing and shell out many weeks of paid leave w/o needing nanny govt to either force their hand or chip in. I honestly think 99% of businesses would in these cases. (and imagine the bad press that could occur should a few scrooges not want to).