Professors have definitely been an important part of Classics. First of all, if someone picks up any Latin or Greek text, that text was established (based on painstaking study of the manuscript tradition) by someone who was almost certainly employed at a university.
Then, if the text has notes at the back of it, those notes were written by someone who was almost certainly employed at a university. If it was translated from the original language for a general public readership, then commonly that was done by a scholar in that field.
As time goes by and new manuscripts are discovered, new light is cast on manuscripts already known, our understanding of some aspect of Greek or Latin life is expanded, or the focuses in our contemporary society change, there is a periodic need for new such editions, and we generally look to scholars to do all that instead of just anybody out there.
It's the wage-earners competing in a pseudo-meritocracy, just like fifty or a hundred years ago. The difference now is that our skilled trades require more formal education.
In the top 10, 2 are 1st-generation trust-fund babies (The Koch brothers), 7 are tech company founders, and 1 is self-directed investor. Certainly most of these enjoy great upper-middle-class opportunity and privelege, but these founders did not get their wealth from pedigree-appointed positions at Daddy's company after drinking their way through a Political Science degree.
Then come 3 more trust fund babies (The Walton kids), a self-made casino founder, and another tech company founder.
In developing countries, humanities can only get you a government job. If your idea is right, as the economy expand and the role of government jobs becomes less important, humanities would naturally decline.
That said, it seems to me that the disruption probably will first be in the engineering areas rather than in the humanities. Do you know chemical engineering? I can test for that, whether or not you went to a university. (The GRE will do that in many fields.) But did you absorb the enrichment that should have come with your university education? The humanities cares about that; STEM doesn't.