Solution

Mothers with small children face a dilemma in that commercial childcare is expensive, so for individuals with low income potential it often makes more sense to stay out of the labor market and take care of one’s children oneself.  Free childcare could relax this constraint, allowing the parent to become employed raising family income.

If the 100% subsidy for childcare were phased out as family income rises, then this program would be subject to the poverty trap, but as long as the net price of the program was less than the parent’s earnings it’s likely the parent would stay in the labor force.  This suggests the policy would be worth pursuing.