I think you are right that that is the best option of all. I do predict, though, that if the private sector were allowed to make all the decisions by itself, they would for sure find that STEM majors are much more practical to finance than the majority of other types of majors, though of course there would be some notable exceptions in economics, pre law, business, accounting, finance and a few other areas (note I am counting pre med as STEM here just to avoid confusion).
If there were only private lending, bankers would overwhelmingly look for collateral from cosigners (parents), as makes perfect sense.
Beyond that, the caliber of school and student matter far than study plans and long-range goals.
(And pre-law is a goofball major—most solid law students come with a history or English or some other substantial, traditional major.)
But yeah, point taken—EE majors are less likely to end up as baristas after graduation than are sociology majors.