The whole Economic point of free schooling is that people with a higher level of education can do work with higher value added, so better paid and also generating more wealth, hence they naturally end up paying back their education (and then some) because of the higher tax take, both directly that they themselves pay and indirectly because it enables more companies in high value added industries.

In other words, it's an investment in people by the State.

This of course, only works when the economic environment actually uses such more highly educated people to generate more wealth using their capabilities for higher value added activities, which isn't mostly the case nowadays in most of the West (you really don't need highly educated workers to be a rent-seeker skimming money from the rest of Society).

By then again, as the original poster is postulating the fantasy and detail-free suggestion of "foster an economy with better-paying jobs" (further below the OP provides "tax cuts" as "detail", which leads one to think maybe the OP has been living under a rock in the last 40 years of ever falling taxes, when the economy actually went in the direction of "worse-paying jobs") I reckon my point requiring an economy geared for production rather than rent-seeking is actually more feasible and less "magical thinking".