It used to be like that, and I'm old enough to remember why they changed: not every student handles exam stress well. And it has nothing to do with their competency in that subject matter.
For example, in the UK, it was shown that biasing course results towards exam marks caused woman to perform worse than men. But when results included assignments, women generally performed better.
This is obviously a generalisation but it is one of the reasons why so many courses now take assignments into account for their final grade.
In my undergrad, a few decades ago, it was typically the case that assignments and exams both were a part of your final score. Often it was something like 40% exam/60% assignments, but this could change.
However what you mention about different people being better in different circumstances reminds of what our maths courses typically did, it was called "plussage" IIRC. Basically, the scores were calculated, and you got the best score from a 40% exam/60% assignment weighting or a 60%/40% (or something, the exact values are lost to time.) So if you were bad at exams but had done the work through the semester, you got a boost. Or if you were bad at deadlines but had still studied, you weren't (too) penalised.
For example, in the UK, it was shown that biasing course results towards exam marks caused woman to perform worse than men. But when results included assignments, women generally performed better.
This is obviously a generalisation but it is one of the reasons why so many courses now take assignments into account for their final grade.