That is certainly one point of view but the legions of highly educated unemployed in Western nations suggest that it isn't actually true.

Educated vs. Skilled

Lots of people have college degrees in fields where jobs simply do not exist. Bachelors in Philosophy, Women's Studies, or Underwater Basket Weaving are admirable but do nothing to prepare you to get a job. Most people who study in fields that don't directly correlate to a job end up having a career in an irrelevant field after on-the-job training.

Being educated and unemployed just means that you probably didn't need to go to college anyway.

The difference between a high school diploma and a bachelor's degree is halving the unemployment rate. http://www.bls.gov/emp/ep_chart_001.htm

Yes, but if we could snap our fingers and educate everybody would the unemployment rate of the newly educated people halve? In other words, can the skilled labor market absorb the excess from the unskilled market without seeing a partially or fully compensating reduction in prices?

It's not impossible but I have my doubts.

No, I don't think that educating more people will make educated people worth as little as uneducated people are now. Educated people are (on average!) more productive, so the economy will be larger and the average paycheck should go up.

Yes, educating workers makes them more valuable. I agree.

No, the fact that a worker is more valuable does not mean they will get paid more. "More valuable" only implies a larger upper bound for what the company would be willing to pay were the employee's skills very scarce. However, almost by definition this is not the case for the majority of the labor market: supply and demand have a much larger effect on wages than productivity. Note how productivity has been rising at the same time as wages have been falling in, IIRC, the lower 90% of US household incomes, so this isn't just a theoretical distinction. For most people in the US it's a harsh reality. It is indicative of our fortunate positioning wrt supply/demand that we can even entertain the thought of getting paid in proportion to the value we create.

Small changes in supply/demand can have disproportionate effects on price, so adding a seemingly modest number of educated people to the market could theoretically send aggregate wages tanking far below where they were originally even if each and every employee was individually more valuable to their employer. I don't think the effect will be that extreme, I'm just stating the possibility in order to highlight how dramatic the distinction between value and wages can get.