This is absolutely true in a free market with no labor distortions (BI, tax, etc). However, we already live in a world with distortions (taxes, welfare, regulations) that drive a wedge between economically optimal and actual choices. How would adding an even bigger wedge help?
Also, due to women's sexual choices, most likely the father is also highly productive. So your "fathers change the diapers" is not really a viable solution - it just means you lose his output rather than hers.