The question isn't whether or not you should have some influence (if it's useful, of course you should), but rather what's most efficient. Giodano's argument is that those 18 year olds (and their parents and other advisors who do have at least some impact on what and where they study) will more efficiently gauge the market than government bureaucrats will.
I think that's true with the caveat that those bureaucrats will be able to foresee some ways in the 18 year olds will be incentivized to make poor choices (at least from the tax payer's perspective of poor uses of public funds), and can incentivize choices in the other direction. Which seems to be what you're advocating for.
So, to Giordano now: yes, free markets are more efficient than central planning, but a regulated free market can be more efficient still.