I don't think it's a lack of educational opportunities. Not as such. It's several things.
* Machines used to enhance the productivity of a single person. Computers just replace people, and not with another person operating a computer to do what multiple people once could, with no humans at all.
* As you noted, "the masses" can only adapt so much. We simply cannot make a scientist or a fine artist out of someone with an IQ of 85, and that person is only one standard deviation below average. Hell, we have a damned hard enough time trying to make a high-level white-collar worker out of someone with a merely median IQ of 100.
* Our socioeconomic system is structured so that the productivity improvements from computing are captured by capital owners (broadly: businesses who own machines, business owners, and investors). So instead of higher productivity raising output, increased output making the worker more valuable, and the more valuable worker commanding a higher wage (what we used to get: wages rising with productivity), we now use productivity as an excuse to lay off unwanted and "unnecessary" workers, keep output at the same levels (or grow it only slightly), and pocket the difference.
* The "rote bullshit" jobs being replaced by the machines are, in fact, the limiting factor of the economy. Scientists, artists, and philosophers in fact depend completely and utterly on functioning infrastructure and basic industries. To paraphrase Paul-Muad'dib Atreides, he who can destroy a thing has supreme power over it: the businesses that control the basic infrastructure on which the "higher-level" occupations rent-seek upon it. So we can't seem to have a market economy in which we pour all our productivity advancements in "raising the level" of occupations people hold. Today's prices bear this out: housing, health-care, education and energy are the most expensive and quickest-growing components of a common budget.
At some point, we have to accept that many (most?) people are too dumb to work in a mostly-automated economy, that we've given the base of our economy entirely into the control of a narrow class of capitalists, and that these two classes of people hold the remaining productive/"higher-level" citizenry by the balls.