For all these "it is better" points, it still doesn't even begin to outweigh the "you get to spend time with your children" point. This is the most important part of child rearing and once they've moved on you'll be thankful you spent your time with them instead of... whatever all that income/societal optimization stuff is. You get to raise your children once.
Who is 'you' in this context?
If one parent is working, the other home with the kids, chances are that the one working can't take as much time off or has a harder time setting a healthy work-life balance (increasing your pay requires working harder).
Using myself as an example: the only reason I can pick up my kid early from the kindergarten and spend quality time with him is because I can afford to not work 9-5 every day due to my wife also working.
Not sure I’d apply your situation to every parent.
As most things it is a balancing act. Children also need to socialize and learn to operate in a social setting independently from their parents. Day cares have an important role in this aspect in our nuclear family based societies. Confining children to be paired to their parents all the time is also not going to be good for their development.
I guess you missed the part where I said that it is better for the child. Reducing my argument to "income/societal optimization stuff" is arguing in bad faith.