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.
Any policy (UBI or others) must take into account the state and potential of the country. Based on the Gulf state UBI example (if correct, I did not check) it would mean that with their initial conditions UBI will not result in developing skills (although, thinking of it, maybe their purpose of giving UBI was close to the one observed, their ruler don't strike me as very progressive).