As for majors, there are limited admissions into some programs such as engineering and business, where you are not formally admitted until after your first year, and have to make a certain GPA. Not all majors had such requirements.
Then there were some unique situations. Majoring in music performance required an audition, and the incoming students tended to be playing at a very high level.
This is interesting and I know there was some studies performed, not on the program, but on the school. IIRC, the results were that it wasn't the school that contributed to success, but the person. Meaning, if you were accepted to a top-tier school but attended a lower-tier one, you had as much success as the people who attended the top-tier school. So, as you say, the schools were already selecting for those who were on a trajectory to succeed. There was a caveat that the school did provide more help if the person was from a low-socioeconomic background, and I've wondered if that is due to network effects.
However, it accounts for things like dropout status, so I don’t think your hypothesis fits the data.
Observational data is great for explaining things after the fact. It must be handled very carefully when used for predicting things before they happen. But if you can identify the most likely confounds and eliminate them, you may still be able to answer a lot of useful questions to a fair degree of certainty.
The value is sort of in how the degrees are used as well. Increasingly, they're being seen as licenses of sort, even though that might not be the intent of the program or even reflect the actual experiences of the person in college. That is, the ROI is due as much to the marketplace as it is the degree itself. If HR departments decide that understanding of DL/AI requires a degree in comp sci, even if someone did an honors thesis on that as a psychology major, demonstrating a new proof-of-concept DL model, it doesn't matter what sort of talent is being recruited. Is it the degree holder, the degree, the program, or the employer?
I feel like college degrees have become this kind of signalling label, like much of the modern world, like clothing or something. That's not to discount the skills one obtains as part of a major, but it hurts the person who is going outside the box (in a good way). There's also something disingenuous then, about treating degrees as a resource to be obtained, when the value of that resource is entirely dependent on the way it is treated by others. That is, a hammer is more useful than a rotting stick, but if for whatever reasons there's rotting stick mania, the ROI will be greater for the latter. That doesn't mean the ROI analysis is wrong, but it might give a misleading impression about why.
I admit I didn't read this in enough detail, but I had other questions as well. For instance, in other similar analyses I've read in other outlets, they've explicitly ignored people who have graduate degrees, as it muddies interpretation. But isn't that important? What about the person who gets an undergrad degree in psychology, but then pursues symbolic logic programming and DL models in their master's program in comp sci? Or who goes on to medical school? Some of these degrees, like philosophy, are notorious for being pre-professional degrees, and comparing a BA-only philosophy grad to a BA-philosophy + JD is a little odd, both because it's unfair, but also because the person who gets a BA in philosophy and then stops is maybe different from the person who gets that degree as part of a longer-term plan that includes law school.
There's definitely a bit of insurance and fallback with having higher education that isn't measurable simply by some ROI analysis.
There are a lot of jobs you will never be able to apply to if things go south simply by not meeting the minimum requirements. I was considering a dirt-cheap online MBA once simply for this reason if my biz stuff died (did not pursue).