@Ikari
Yes--they will allow it for a very limited range; which actually concedes the feasibility of it. However, they will never admit this model could be expanded for the entire degree system, as it would destroy the business model immediately. Though, consider, if it is possible to 'placement test' out of Single Variable Calculus, then it is possible to design a test(s) on par with the entire Undergraduate Mathematics curriculum, which would demonstrate proficiency worthy of earning a BA/BS in the subject.
You gotta pay for the slip of paper that says you know the subject, lol.
You can certainly make tests that would represent some aggregated knowledge one should possess when graduating undergraduate university. Certainly in fields, at least mine, there are PhD prelims that one must take in order to be successfully accepted into a PhD program. Those prelims are a aggregate test of knowledge through the Master's level. If you "pass" (no one wins in the prelims, lol) then you can move on with your degree. So I don't think it's a question of "can we". Certainly you can make a barrage of a week long testing cycle to go through all the courses one should take when getting a degree. The real question is "would we?". And the answer is no, we won't. And I think there are a few reasons for that.
First, I think it is, as you stated, based somewhat on income. You pay to go to undergraduate, you spend 4-5 years and pay tuition for those years, you successfully complete your course load, and then you graduate and get your degree. There's a lot of money tied up in that.
But also, I feel that there are other things that go along with a proper University education that isn't summed up in just the accumulated knowledge of any particular subject. The education you receive is meant to be more far reaching than just the degree you earn. So for instance, I majored in Physics and Chemistry with minors in Math, Botany, and Political Science. But my education wasn't restricted to just those subjects. I took music and art, history and religion, tons of English (I actually had enough credits for an English minor, but there was no more room on the form, lol), etc. My B.S. degree doesn't just mean that I took some particular form of science, but that also I had a broad and well grounded education in other subjects as well.
For certain subjects, like science, there are labs and research to be done that cannot be accomplished with a test alone. There is a lot of learning to be done, as well as preparation for either graduate school or a career. One can know a lot of things, but implementing them is different. There are quite a few skills that are learned through the course of an undergraduate education that are not captured in tests alone.
Also, there's the personal growth one goes through during the tenure of their undergraduate stay (or, rather, should go through). This experience and growth cannot be tested for, and indeed can really only be obtained through first-hand experience. Not only is one supposed to learn their subjects and other subjects, but to grow into a well-rounded and grounded adult. There is more to university life than just the base learning of one's major classes. There's socializing and leadership roles, there is personal and emotional growth. All these are summed up in the degree you ultimately possess at the end of the process.
Now, in the modern era is that true as much? I'm not sure because undergraduate education has started to become a "standard". You "have to go" to college now. When I was in graduate school, I had to teach labs to the undergraduates and man...so many of them I didn't feel belonged there. So the commonality of it has cheapened it somewhat. And I do think that on some level it's become more of a "factory", as it were. You go in, you jump through the hoops, you get your degree and leave. People do not treat academia quite with the respect and diligence that they should. So are the things I talked about really summed up in a degree anymore? I like to think that the degree still means more than just mere tests. So in that, I do not support being able to essentially "test out" of undergraduate. The process and the diversity are still needed.
That being said, I don't think people should treat it as if "they deserve it". I think that overall, University has become far too whiny and has lost some of its meaning and some of its integrity. No one "deserves" to go to university, and if you cannot hack it, you should be thrown out. On some level, I do think that we need to restore the mean streets of academia.
So in short. Could we develop a test that could assess if one knows the cumulative knowledge of a subject matter they should learn while in university? Yes we could. Should we do so? Should we allow one to "test out" of college? No.