What qualifies as a good college, for this description? Typical state school, e.g. Oregon State University? What counts in the 5:1 ratio? Because it sure isn't just teachers, that's probably more like 50:1.
Even more time is saved if we unbundled university education in general, so that the various paths and credentials are their own thing. IE, Intro to Poetry 101 isn't necessary for someone who's pursuing finance credentials.
How do you figure that?
Mean class size at a university is probably in the neighborhood of 30 students. Yes, there are some classes that have monster, 200+ class sizes, but this is also balanced out by senior- or grad-level classes that have a dozen students in them.
Students also take several classes, and on average, each instructor only teaches ~1 class a semester (especially consider research professors who may not teach a course every semester). So if students are taking ~5 courses a semester on average, I'd expect to see a ratio somewhere around 6:1, nothing even close to 50:1.
I went to University of Washington - if it matters.
Let's say 25% (a fourth) of them end up attending this magical national public college. That's a 3000000 / 10000 = 300:1 ratio of students to teachers. That's a lot of students per PhD to handle, for a $100k salary with greatly reduced career prospects in academia, since they are not doing any research.
By comparison, the student/faculty ratio at a typical "good" college is about 5:1. Even knocking down the projected enrollment one order of magnitude (so 1/40th of the college-age cohort) gets you a 30:1 ratio which is still 6 times worse.
Feel free to point out a flaw here, but I don't think this plan will work. Basically, you'll end up doing a MOOC site, but those...already exist?
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[1] https://www.insidehighered.com/news/2020/12/15/what-do-new-p...