If you take AC motors, and fail, and study your ass off and six months later can pass it with 100%, shouldn't that really be... your actual grade? Isn't a grade supposed to represent your ability and understanding of a topic?
And then almost magically: health problems, study problems, (most) test anxiety, and other problems no longer actually matter.
University education largely isn't about certifying that certain students know certain things. It's about showing that people who possess the degree meet a minimum IQ + trait conscientiousness cutoff, so that employers can preferentially hire those people.
Grades have several purposes in this framework. First is to drop low-employee-quality students so that the signal for the remainder is stronger. Second is to allow honors and GPA to provide multiple cutoff-levels to fine-tune the signaling. Third is to force re-taking of classes to extract more money out of folks who want to substitute it for IQ + effort.
As it stands, your proposed change would simply increase the amount of work that is allowed to be used as a bid for class position. That's not particularly helpful, IMO.
I guess you could sum it up as: the best test of whether a person is capable of creating something of value is to ask them to create something of value and see what happens.
Besides, taking a month to solve a single calculus problem that should take 15 minutes is a pretty good demonstration that you have not mastered the material.
Also, students are rampantly cheating by leaking previous tests. I saw it every day on campus. TA's leak tests to students and they're printed out before every exam (as the risk is too high to NOT look at a test in advance because your grades = your future in college). I've literally been in classes where everyone had last semesters final printed out... in the room before we took the current final. So the impetus is already currently on you, as a teacher, to have tests with permutations to prevent cheating.
Additionally--while I'm sure many teachers would object--tests shouldn't necessarily be written by the teacher. The teacher isn't teaching their own class, but a class meeting the departments requirements. So if students are being prepared (and not learning very specific permutations of general topics) they should be able to solve problems written by other teachers / test makers. So (on the bright side), teachers shouldn't actually be burdened at all by the testing. That could be someone else's job.
Now, of course, all of this has plenty of practical considerations that would need addressed. How do you permutate a QUALITATIVE question? And how do you easily grade highly permuted (per-person) tests? But just because there are unsolved issues, doesn't mean the underlying (god forgive me for saying using this term:) "paradigm shift" is unsound. It's just different and requires some new solutions to new issues.
But as programmers, we of all people, should be able to figure out how to further automate testing. But I think we really should decouple the idea of "testing" from "occurs at the end of class." I mean, why do we test all finals at the same time during the super-stressful "finals week"? Simply because it's practical. Except it was designed as "practical" before computers and automation were within the hands of every living person. Surely, students would test higher if they could study for a single class's test at a time and without worrying about it occurring during a family or health episode.
And what's a test for except hopefully proving that a student understands the material--but we all know thanks to "teaching to the test" culture that many students can cram for a test and then forget it within a month. But now I'm getting way off the original topic.
My thesis statement is simply: Re-testing finals is practical in modern environments and beneficial and incurs (almost) no additional flaws that the current setup doesn't also exhibit--like cheating.
There will always be cheaters. That's why companies, as part of the interview process, ask basic knowledge questions. It weeds out a lot of the cheaters and frauds. I hear people all the time desperately try to justify cheating. I don't care if people cheat, but I wouldn't hire any of them, and I doubt many employers would.
Sure, there'll always be bad tests and bad teachers. If one could be "taught to the test" then it's a bad test. It can certainly be true that one could pass the test and yet fail to understand the material, but I'm not convinced that people can master the material yet flunk the test.
But testing, in general, works. For me, I know that the pressure of final exams would motivate me to learn the material. No pressure, no learning.
40 years after I graduated, I'd surely flunk every final if I retook them cold today. I just finished taking the MIT 18.01 calculus class online. I was surprised at how easily the stuff came flooding back into my head. It's still there, I just had to chip the rust off :-)
I personally found doing problem sets and being able to check my answers immediately to be the best way to learn. There's no point to just copy the answers if homework is ungraded. If students feel no motivation to do homework to learn and practice, that's on them, especially at the college level.
If you don't grade exams but grade homework, then homework just becomes a take-home exam...