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.
I generally agree with you, but often the reason that these programs work economically is that those who don't choose to use them still contribute. There are (at least) three different categories: (1) caregivers who will care for their child themselves regardless of whether or not free care is available elsewhere, (2) caregivers who will find care elsewhere regardless of the cost, and (3) caregivers who will make use of free care if available, or otherwise, care for their child themselves.
I think the group (1) has a tendency to be higher income. It's certainly not true of everyone in that group, but I would wager that a significant number of people in that group do not need the financial assistance. Those people not using the free resource, but still contributing to funding it is what makes it economically viable.