Capitalism alone doesn't do that either though? Doctors, bankers and rich people's children get rewarded. Nurses, public restroom cleaners and teachers don't.
Right, but we should. If the state's purpose is to do things like provide education, the state needs to make it worthwhile for people to do the work of education. Despite what some people claim, capitalism is not the solution to every problem. But at the same time, if citizens are apathetic about education, they won't want to pay for it.
It's one of those weird catch-22s. If we actually incentivized those jobs nobody wants, they'd get done better, and then people would be more proud of the work, and be willing to pay for it. But because people don't pay for it, the work is done poorly, and so people aren't proud of it, and thus don't want to pay for it.