however, my understanding (though i can't speak for the other commenters) is that the reasoning behind "humanities-educated people make better democracies" is NOT that humanities-educated people are more virtuous, and thus will willingly not degrade the commons (the reasoning you seem to be criticizing). rather, it's that humanities-educated people cannot be manipulated as easily by a demagogue (and other similar things).
the usually cited problem with democracy is that it gives the people the power to choose, but it does not automatically makes them capable to make good choices. that's where the education comes in.
clearly many questions require technical/domain knowledge to be answered and are not simply a matter of preference. for example, fixing your car, or building a bridge. and even running a business or cooking an elaborate meal. with technical knowledge, you are able to make better decisions whatever your preferences are. humanities education is then implied to be the "technical knowledge" for participating in society.
of course, in that case, we can discuss what should be the content of the "humanities education", but that's another discussion...