"If capitalism is so great, why doesn’t it pay people enough that the government doesn’t have to get involved at all?"
Don't confuse our present neoliberal system with capitalism. They are not the same at all. Neoliberalism assumes that all necessities will be provided by the "free market" and that government's only job is to provide funding for those markets via its power to create currency, even when the markets fail or prove they are not sustainable.
Capitalism simply lets the free market live or die on its own merits while assuring citizens of some basic rights as spelled out in our constitution. Many of those rights require individual or group funding by government as a safety net, but the markets are not supported, and their actions are regulated so as to not cause harm to the individual or the society.
If any individuals are worthy of support from our government it is mothers, as they are the ones who will shape our society's future. In a neoliberal economy they are just another number and expected to "earn" their own way as well as support their offspring. This, of course, means full time (or more) creation of profit for a corporation with no consideration for the added burdens placed upon them by the expectations of the society concerning the care of their children.
In a sovereign currency issuing nation there is no reason to not give every type of support, financial, mental, and moral, that our mothers of our future generations need to advance society with the talent and intellect of their children. No ones taxes need to be raised and no borrowing needs to take place to "fund" doing so. Our money is infinitely available to Congress when it spends, even in absence of any revenue, so any failing that can be mitigated with money is entirely a political, not economic, choice.