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.
But this is true in the other direction, too. Means testing costs money, time, and ensures some needy folks fall off the program.
For example, Florida did drug testing as a condition for welfare benefits... and it cost more than they saved. https://www.nytimes.com/2012/04/18/us/no-savings-found-in-fl...
It's more complicated than that. Of the 6352 people who applied for TANF, 2306 dropped out during the process. Then of the 4046 TANF applicants remaining, only 2.6% tested positive for drugs. The vast majority of media coverage focused on the 2.6% being less than the ~8% drug-use rate in the general population.
What we don't know is of the people who dropped out, was this due to unintended reasons (privacy concerns, the inconvenience of the drug test, missing deadlines) or due to the intended reason (people self-selecting out because they knew they would test positive and become ineligible for 12 months). We'll never know the real breakdown, but it's misleading to say "it cost more than they saved".