if high school diplomas are worthless, then there would be no increase in pay for those who have them over those who don't. according to your own evidence, it seems a high school diploma is worth about $7500 a year, or an additional $225,000 dollars over 30 years aka a house. You claim that it is the scarcity of degrees that make them more valuable, but that ignores the part that there has to be a demand for them, toxic waste is pretty scarce but it isn't very valuable because nobody wants it. If a degree didn't offer something employers wanted ie an education, then those that hold those degrees wouldn't pay more for them. An example is social workers, they require college degrees but since nobody really wants them (though we do need them) even with a college degree they get paid poorly compared to other degree holders.
You claim in the same sentence that requiring everyone to have degrees would lower the median income yet drive up inflation. Generally, you can have one or the other baring all outside influences, the less people have to pay, the less businesses can charge for something.
i also maintain, that if you take someone who previously would only get their high school diploma and send them to college for two more years to learn more math, science, computer skills and such, they will become a more valuable member of society.