> Let's assume that all those new laborers get paid and therefore demand also increases, moving the equilibrium so some of the wage stagnation pressure is dampened. It's still not going to offset the effect of new labor and taxes

Let's not make the absurd assumption that parents continuing their careers and more daycare centres in operation must be net negative for economic growth.

Even if that was the case, the alternative proposal to subsidise parents equally large amounts whether they use it to pay for childcare or not would result in a larger tax burden paid for from a smaller economic pie.