Until everybody does it. Then you need that shift just to be able to afford to live where you would have without it, and to be in the better school district you need a full time job as a second income. Then everybody does that and we have the two income trap, and the option to just be a stay at home parent evaporates because the other families have two incomes and you're bidding against them for positional goods.
And it's no answer to ask each parent to work half as much and then split the child rearing duties, because that's still an economic disadvantage relative to the family where both parents work full time. It's even worse than having one full time worker and one full time parent, because one full time job pays more than two half time jobs due to the reduced training costs and other administrative overhead.
So instead it creates the requirement that women become full time workers in addition to full time parents, only to have the same quality of life and economic stability they used to have as stay at home parents. And we see fertility rates and female happiness on the decline since the 1970s.
A possible solution might be to fight against scarcity in existing positional goods. So make housing costs low enough that anyone can afford to own a home even with one income or two part time incomes (and build lots more homes to make that possible), untie school quality from housing and let people send their kids to any school they want to as long as they can get the kids there, etc. Another (complementary) option is to increase support for families with children, e.g. bigger child tax deductions/credits. But we clearly need to do something -- we shouldn't just pretend it isn't happening because it's politically inconvenient.