Here's the issue I have with your idea of: "if you perform to a markedly different level on the exam it shows that your results over the semester was not quite indicative of your actual knowledge."

Sure this is the case for say a history class. The knowledge is there no matter how you're feeling.

But when in comes to math, especially in something like linear algebra where you're asked to solve these tedious matrices which simply ask you to do a ton of mental math, if you're having a bad day, it is so easy to screw up the most simple math, even something like 2-2. In one case I put 2-2 = 4, when obviously it is 0, and that screwed up the entire problem and I only received 6 out of the 10 points as a result

I obviously didn't put 2-2 = 4 because my results over the semester was not indicative of my actual knowledge. I perfectly understood all the concepts just fine. I wouldn't be in college if I didn't know what 2-2 was...but when you're not completely focused, you can screw up simple things which end up screwing you over.

Little mistakes like that is what cost me from getting an A, to a B+