A billionaire can't wave their arms in the air and make nannies sprout from the ground like mushrooms. The nannies have to come from somewhere else where they were doing something else.

If families are feeling the pinch, that "something else" is probably work that was important to setting up families and maintaining a standard of living. Forcing billionaires to put money into childcare is just making it more difficult to have children because those resource aren't going to be going towards whatever the more pressing problems are.

Billionaires make all that money by making things happen that people need done. Disrupting that and sending the resources to childcare is not likely to work either. If the problem is that childcare is too expensive, what is important is bringing down the cost, not trying to find someone else to pay the cost. There is no-one else, having children is too common an activity.