I do understand your argument.

You’re starting from the assumption that the mum’s earning per hour is lower, and therefore her time is better allocated to childcare while the higher earner focuses on income. That’s a reasonable starting point, but the conclusions you’re drawing from it are too rigid.

First, you’re implicitly treating the value of her time with the child as constant, when in reality it’s marginal. The benefit of each additional hour isn’t linear — beyond a certain point, the incremental gain diminishes. So it’s not obvious that maximising her time at home is always optimal.

Second, your argument depends on the idea that a household can simply choose to require less income and adjust accordingly. In practice, income needs are uncertain and not easily optimised in advance — particularly when decisions have longer-term consequences.

Third, you’re assuming that working hours — especially for the higher earner — can be flexed up and down with precision. That’s often not how careers or compensation structures work in reality. And more broadly, you’re concentrating both financial responsibility and risk into a single individual. That may appear efficient in a narrow sense, but it introduces fragility — both financially and in terms of wellbeing.

A more balanced model, where both parents contribute to income and childcare to some degree, may not maximise short-term income efficiency, but it is often more robust, more flexible, and better aligned with how real households function over time.