Regarding your first point: since you already stated you're sometimes in favor of publicly subsidizing things like vaccinations and criminal incarcerations, your opposition to publicly funded education must result from this distinction you draw between public good and "private enjoyment". But I think rather than just assuming a position on college degrees a priori there is a rich and valuable debate to be had about whether higher education should be considered a public good and not merely a private enjoyment.

And your second: this seems to be both a distraction (I don't see how arguing that an educated citizenry is a necessary ingredient of democracy implies that one should necessarily agree with denying participation to those deemed incapable) and somewhat misguided (seeing as we already do deny the right to vote to a certain class of people unable to make correct judgments--we call them felons).