I think this will actually have the opposite effect that you're looking for. If you dramatically increase the supply of educated workers, the financial returns of getting that education go way down, for each individual worker. It may be a good thing for society and help us achieve a lot more collectively, but it's not a good thing for the worker. You'll end up with all the wealth pooling at the people who own the companies who employ these workers - much like now, but worse.
To increase wages of middle-class workers, you need to increase the demand for middle-class jobs relative to the supply of workers available. There are three main ways of doing that:
1) Increase demand. Create many more companies, which will force them to compete for talent and raise wages or be left without a labor force. YC and other accelerators have been good for that, and you see what results in San Francisco (although engineer salaries are arguably artificially depressed at the moment because companies form a cartel on wages and nobody has yet defected to try and corner the market).
2.) Decrease supply. Take some workers out of the labor force, either through converting them into employers through entrepreneurship, encouraging families, legislating a shorter work-week, or discouraging education. Note that this also will reduce output, which is a tough sell in a global world.
3.) Join multiple independent workers into one firm. This is basically what labor unions are about, surrendering your autonomy as a free economic agent so that everyone has better bargaining power.
Productivity gains, when spread across a whole class of people, never end up being captured financially by the group they most apply to. All the surplus is competed away, and the people who most benefit are the complements, those goods that everyone in the group depends upon. That's why increasing rates of college attendance - and they have been increasing, dramatically, at least in the U.S. - have resulted mostly in rising tuition and lowered wages.