All the angst appears to be emanating from people for whom it is axiomatic that mental load be shared 50:50, and yet it can be proven that this will make any household poorer. Very few people want this.
Also, I'm not convinced by this at all. Young women are now more highly qualified than young men and out-earn them collectively until they have children. There is no reason that once people have families one person has to focus on work and one on home to make things efficient.
Currently, due to the structure of our tax system, childcare system, sex stereotypes still prevalent in our society etc the situation changes when people have children. However, these things are choices we have made on a societal level. Other systems exist.
If we look at some Scandinavian countries where the social structures above are different there is a far more equal split in terms of both earned income and household responsibilities between couples with children. And last time I checked the people living in those countries were not poorer than those in the UK. They also generally outstrip us generally on measures such as: lower divorce rates, higher childhood wellbeing scores, higher general happiness of population, higher education scores for chilren, population health, life expentancy, etc.
These things are not inherent and inevitable; it is possible to structure society differently so that households are not financially disadvantaged by both parents maintaining careers and pulling their weight with household tasks and children. It is a cultural and political choice to structure things so as to encourage the continuation of women having lower earnings and doing more of household tasks than men.
I'd also question your assertion based on the economic aspect that nobody wants a more equitable system. I think it's clear from many posts here that a great many people do. And even with our current structure which makes it difficult to achieve, will often make decisions that don't maximise the "economic output" of the household because that is not the only factor in the decision: the wellbeing of the people in the household is also important and this is not determined by income alone. And in the long term, as we all know, it is very dangerous for women to fall into low paid/ no work and focus only on home life. I shudder to think how my children would be living now had I do so.
So it appears to me that what needs changing is the structural system that currently exacerbates these problems. Affordable childcare, tax equalisation, flexible working, proper parental leave for men, enforced and much higher CMS etc all need a radical overhaul so that peverse disincentives and penalisations are not determining/ influencing people's choices. That's not to say people can't decide to structure their household as you've suggested, but that the system should not be structured in such a way as to effectively force some people into that situation when it's not what they want.
These changes are long overdue, as well as obviously people raising their daughters not to tolerate inequality, and their sons not to expect a female house servant and to expect to pull their weight in all aspects of life!