Taking time off from your career puts you behind your peers. That's no surprise. If women take time off to raise young children that hurts their long-term earnings. Again, no surprise.
If we want to frame it in purely economic terms vis-a-vis government:
Does the long-term increase in taxes paid by working mothers cover or exceed government outlays to provide childcare, especially in the early pre-K4 years?
Secondarily is there any negative effect on the children and if so can those effects be mitigated?
The study seems to indicate it is a net-win for the government because high-cost childcare only happens for 1-3 years but the earning power increase lasts the rest of a woman's career. I presume rational government policy would attempt to make free childcare tax neutral in this case.
In alternative terms you could see this as the government making a short-term (3 year) loan to cover childcare while being paid back in the form of higher taxes paid by the beneficiaries over the next 20-30 years.
Whether this makes sense for an individual couple is another matter. Whether the government should encourage new daycares or people to train as childcare providers is also another matter that bears some similarities to the universal healthcare arguments (eg that the government would want to encourage more people to train as doctors and nurses since the expected demand for services would increase, though true believers in the free market should expect the market to take care of such problems).