Mike: I'm always cautious when using the word "free" because the term seldom has a common understanding amongst readers - but last century, Australia had "free" tertiary education for a while and it was the principal cause for spawning a plethora of first time graduates from working-class families. My siblings and I were fortunate (and honored) to be among their number!
As for "limiting it only to those who actually want to strive to pursue a particular set of skills" - even if there was a process for analyzing a student's intent for entering a university - I'm not sure that it's the role of educational institutions to do this. And notwithstanding my foreigner status, particularly in a litigious country like America - I'm not sure that these institutions would take-on this accountability (or does America need another reason to further line the pockets of litigators?)
Rather than focusing on student's intent for entering universities, a more achievable and far better metric is assessing the student's scholastic abilities as a rough surrogate for their capacity to complete studies. Of course, a student's academic prowess (which most definitely is not their IQ) does not equate to their willingness to apply those abilities to studies - but it is a not unreasonable decider for university entry . No problem with the risk of an avalanche of unworthy students because the pass-level for entrance examinations can be tailored to the number of available places. And no problem with accusations about ethnic, or wealth discrimination because everyone is dispassionately treated the same (thereby aligning with your Mr Jefferson's credo)!
Apart from a will of citizens to do it (thru their votes) -one of the reasons why "free" (there's that word again) university was achievable in Australia for a time was the fact that the tertiary institutions were owned and they were directly funded by Government (yes, it was rather socialist in nature - but certainly not in name). So it was simply a case of diverting a greater portion of the tax purse to this new initiative. Not sure that it would be quite this easy for America's education model?
Don
In the UK we had "free" university level education, with a points based admission system.
As I remember it (25 years ago now), essentially you apply to a number of universities and they give you an acceptance offer - the number of A, B or C grades you had to achieve in your A-Level school leaving exams for guaranteed acceptance. You then ranked those as your 1st, 2nd, 3rd choice etc. in the system.
(If you missed the target of your offers they would sometimes reduce their offer, or you could find alternative courses via the Clearing system).
As this potentially meant anyone could go to uni, enrolments increased, so universities expanded and offered more and more courses and places.
Then about 20 years ago, due to a looming funding crisis, universities were allowed to charge
tuition fees direct to students, rather than local councils covering it through taxes.
It started at £1000, and is still capped, but currently in England students can pay up to £9250 a year for tuition, so with typical courses lasting 3-5 years, just tuition can cost between £30 and 50k, before you even think about living and accommodation costs.
This has led to a lot of university courses offering places to students with incredibly low (or non-existent) criteria for their offers as there are now more places than applicants - so we've gone from a growing system of free education to a shrinking system where admissions are largely down to whether you can afford to pay for the course, rather than whether you're academically suited to it.