You'd also really have to look at the breakdown by income level. Worldwide, female participation in the workforce is actually higher at higher income levels.
That just means that contemporary woman is not seen as shirking her mom responsibilities when working. While the children are definitely seen as mothers primary responsibility, working is part of that. It also means that there is less expectation on women to be artificially nice or helpless and dependent compared to American stereotypes.
Unlike in America, woman working is not interpreted as woman being anti-family. Unlike in Germany, mom working is not interpreted as mom failing her kids.
Also, it is not like the first women stepped into Russian factory only after revolution. The women did worked prior that, obviously. Whether on rural farms in villages or in factories or as cleaners or selling stuff at marker etc. The aristocracy expected women to not work, but generally Russians have been poor and had to do stuff to survive.
I have never thought of having more women in the workforce as "anti-family", and will definitely research on that, but personally I am happy to have a more diverse workforce and not stigmatize men if they want to stay at home.
I dont think Eastern Europe is the place more accepting of men staying with children at home.
In lieu of their mothers, children need to be looked after by professional caretakers. This weakens their bond with the mother. And even in the evenings, when mother is back from the job, she's beat and can't give the same level of attention to their children.
https://data.worldbank.org/indicator/SL.TLF.CACT.FM.NE.ZS
That doesn't falsify your specific claim, which is about a very small fraction of the population (six figure salaries put families into the top 3% or so), but it's reasonable evidence.
Broadly: you're taking a cultural point about upper middle class "America" and extending it to the whole society. Most people don't (can't) live like that.
Childcare price is issue too and sometimes pushes opposite way. Poor families in America sometimes have to stay at home, because childcare is expensive.
Staying at home is not just function of how much you earn, probably not even primary. There are also practical aspects of "is it expected of me", "is it possible to manage school, activities and work" and "do I want to stay at home".