My wife is a stay-at-home mom. We are lucky that we can afford to do this. Most of our kid's friends have both parents working and they pay for child care. If suddenly they were able to have that childcare paid for, that would be wonderful! It doesn't affect our situation at all. Why would we oppose it? I don't need to have my own "waiver" payment in order for me to be in favor of my neighbor's burden being lifted.
It's like free school lunch. We pack our kid a lunch every day, but some families rely on the school-provided free lunch. It's never even occurred to me that we should get a $3/day payment because we don't take advantage of free lunch. Having free lunch available is unequivocally a good thing, regardless of whether we personally partake.
Even if we consider it as an "efficiency" problem, it is far cheaper for a person to be paid to take care of N children (where N is not too large), rather than have the have the mom, who is probably qualified in some other field, take care of just their children.
> the mom, who is probably qualified in some other field
Parents are plenty qualified to take care of their kids. And their qualifications in some other field doesn’t mean that working that field is better for them or their kids or the country. Having strong family structures and time together is pretty valuable.
"Why should I pay for taxes that don't benefit me?" is an aggressively American view toward the social contract.
People who make money pay taxes, those pay for things, and citizens (not taxpayers) get to use those things if and when they need them.