The problem sets that you usually get in a university course is a small fraction of the exercises in your textbook. Which raises a question: do you need to solve all the exercises from your textbook? Maybe the author just presents a lot of them so that your professor can choose those that fit his course.
I'm looking for a reason not to do all the exercises, or even only do the course's problem sets (a small fraction). For example, Pugh's "Analysis" claims to have more than 500 exercises—that's way to much; I think the bulk of them is not essential. The main idea of studying mathematics is to learn new mathematical concepts, and not get bogged down in routine computations.
What is the reason of the problem sets? Maybe just to check that you understand the concepts well. But maybe the problem sets are so small because they are meant to be checked by some person, otherwise they would be bigger.
EDIT: Especially it relates to the courses that you need as a prerequisite for the other much more important course. For instance, I need Linear Algebra as a prerequisite for Analysis. When I get to Analysis, I will do all the exercises. But I don't want to spend a lot of time on Linear Algebra—I understand the concepts, understand the proofs, and that's it.