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.
For example, if you lose too many benefits when you get a job, it can easily make getting a job yield negative expected value, this is bad because often it stunts future career potential.
There may be families that cannot quite afford to be a stay-at-home mom even though they want to. Providing the waiver also increases the overall fairness. In rural areas there are generally far fewer childcare options, so this becomes a benefit that accrues to those that live in cities. Not very fair.