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.
It is bad faith reasoning. If you imagine a person that does not want women to participate in the workforce but wants to express that in a way that doesn’t sound repugnant, it is pretty easy to see how someone would come up with that.
The way you can tell that it’s bad faith is by looking at the context that “pay women to stay out of the workforce” gets brought up. In this case it is framed as an alternative to providing childcare, but those two ideas have nothing to do with each other. As a society we could do both. The “pay women to stay out of the workforce” or “pay for childcare” dichotomy is completely made up, and folks that engage in that particular type of make-believe are either profoundly intellectually lazy or being intentionally disingenuous.