This exactly - I was a single mum working full time, my children had a secure, happy home, and still do, 20 years later!
Having a mum at home when children are at school does not make the home any happier, or run any smoother, or the family have more social life, or any of t he things being trotted out here. The children are at school!
It does make the family financially poorer, and does model a poorer work ethic to the children. It does mean less security when they are older, as the parents are less likely to have secured a mortgage, and less likely to have paid it off if they do
I worked full time throughout my children's child hood - result: mortgage paid off, adult children both came home from uni to a rent free home, and can begin their adult life without any financial pressure. Both have jobs, both are saving for a mortgage, both are enjoying their "inheritance" now, as who knows what will happen in the future, if I need to sell my home for care, for example.
And both are well used to contributing to the smooth running of the home, cooking family meals several times a week, cleaning and washing up, doing their share of laundry, because they were brought up doing that, and it is no big deal to them.
Both have as much social life as they can possibly time table! And both have family time too. When I have been ill and not earning, they have covered the household bills between themselves, without having any mortgage to worry about.
We would not be in this position if I had left work to concentrate on running a home.
It is a crazy idea, you run a home while working. Lazy, and irresponsible to give up work to do it. Nobody else benefits, just the person who gives up work has a lot less to do, brings in no money, meets fewer people, narrows their social circle, and thus their children's, isn't out in the world, knows less of what is going on, understands less, and ultimately becomes dependent financially and emotionally on the rest of the family - gets carried, in other words.