It hurts my ability to design good problem sets if I can't put this fundamental problems on the problem set. There are some fields where there are computations every student should do - and, as a result, they are written up in books and online sources everywhere. It forces us to use more obscure, and often not as good, problems. We had an analysis course at MI last year pedagogically ruined because everyone kept solving the homework problems, so the professor kept increasing his pace, until an in class test revealed that no one was actually doing the homework themselves. The first two situations are obvious, and your professor should be adjusting to it. Either you are falling behind the rest of the class, or other people are turning in much scantier work than you are, or everyone is googling the problems.
Twenty hours of homework a week is very high for a math course higher than I would expect from any course that was not promoted as a "boot camp" style course.
It destroys our ability to calibrate the course difficulty. Let me explain why I, and almost all faculty members I know, do not want students searching for homework problems online.
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