Why do we put so much weight on final exams?
What's the alternative?
Exams have been criticized since before I can remember, but if someone has come up with something better I'm not aware of it, e.g.

Oral exams would &quot;work&quot;, except those would also be high-pressure examinations, and they are also very time-consuming. Furthermore, unless one records the oral exam, it would also be difficult to resolve grading disputes.
Homework-based assessment is vulnerable to cheating, since the student can get 3rd-party help with the assignments and it would not be easy to catch. Students can also work in groups, with associated problems (it's quite common for a few people in a group to do most/all the work and the rest just copy them).
Subjective assessment where the teacher simply assigns a grade to each student is vulnerable to biases (which is part of the reason why grading schemes and/or blinded assessment are common).
Finally, there's a school of thought that if you are unable to reproduce the learned material, under pressure, you haven't actually learned it.