I'm not sure increasing the quality of teaching will do much for outcomes. A little, probably, but likely not much. AFAIK the vast majority of jobs that expect applicants to have a degree, or favor those who do, don't do it because they
need their workers to have a good college education.
I think if we increased the quality of education, say, 20% (let's just assume there's some useful measure of quality here, and that expressing it in percentages makes sense) across the entire country, it'd have only a small effect on employment for grads, all else being equal (i.e. those changes don't also reduce the number of grads per year)
From what I can tell, most people attending US colleges and universities are mainly paying a fee to participate in a scheme that keeps the unemployment rate down by warehousing capable workers in dorms, keeping them out of the "seeking work" category, and those students-but-potentially-workers are doing so because (they believe that) participating in that program gives them advantage in the employment market, some years later... but not exactly to learn anything, which is a secondary concern at best, for a majority of those attending.
I'm dunno how much of it was intended to work that way, but it seems like the main actual thing the whole system is doing now, whatever anyone's intentions were or are. Only semi-reasonable way I can think of to break the cycle would be to decrease the unemployment rate and keep it low for a long time, which ought to get employers to start "out-bidding" the alternative of "go to college, delay career" for recent high school grads, and to stop worrying so much about whether applicants have a degree.
In fact, now that I lay it all out like that, I'm pretty sure one of the core problems with higher ed is that labor is too weak, which has led to some really weird outcomes as far as how higher ed is treated.
[EDIT] Put another way, that seems perhaps less at-odds with itself than the above contention that increased university attendance acts to keep unemployment rates down, while I also think decreasing the unemployment rate might be a way to reduce university attendance—so many people are going to college, because companies aren't desperate enough for workers to offer many "mere" high school grads real money—they can afford to hold out for college grads, even if they don't really need them.