This may be a stupid question, but why is the ability to write pre-existing sorting algorithms from the top of your head necessary in those places? Don't they use standard libraries? Or is it just used as a general test of understanding of the concepts?

I think its a test for the candidates capability to grasp the concepts and coding those basic algorithms with out bugs is to demonstrate their ability for diligence.

I'd focus more on graphs and trees, and having a passing familiarity with the algorithmic and space trade offs of sort algorithms. One could argue over whether it's important philosophically, but from a practical standpoint they expect candidates to know it.