This is a great way to kill a policy.
It would technically be most fair if every parent was given the same amount of money per child, period. Then they could do what they needed or wanted with it.
But doing so would not only increase the costs dramatically (by a multiple) it would give money to many parents who didn’t need it for child care.
That’s great in a hypothetical world where budgets are infinite, but in the real world they’re not. The more broadly you spread the money, the less benefit each person receives. If you extended an equal benefit to parents who were already okay with keeping their children home, it’s likely that the real outcome would be reduced benefits for everyone going to daycare. Now you’re giving checks to parents who were already doing okay at home but also diminished the childcare benefit for those who needed it, which was the goal in the beginning.
They're the ones who are basically paying the vast majority of the cost of this program, what's the problem with a small fraction of it coming back to them? Especially if it reduces the bureaucratic overhead of running it?