It can, until you locate people farther from fresh food markets and closer to dollar store offerings. Then you end up with somewhat educated but obese and malnourished people visiting ER regularly. And with nobody skilled enough to do plumbing in your house.

Post secondary education for everyone may be seen as a silver bullet, but it isn't. Part of the solution is what you put in your education (more general and less particular stuff), the other part is having faith that any system, human or else, ends up regulating itself without external intervention. Blanketed social economic intervention has many limitations, and should probably be reserved to people struggling, for the time they are struggling.