Graded assignments are useful to give feedback to students. And more importantly they force students to work regularly and not wait for the last minute to study.
I think it is mostly the latter. At least -- I rarely got useful feedback other than a little x (best case it would be on the error, more likely on the questions).
Personally, when grading I keep a file of all my feedback so I can easily copy-paste it into their feedback files (since everything is digital nowadays). For a given assignment, usually only a handful of mistakes are made (repeated by each student). If anything, having the file makes my grading more consistent -- same points for the same error.
I'm under the impression that this is a not-unpopular system, but try as I might, I cannot get anyone else to adopt it.
Personally I always preferred quizzes for that. I've always been a very strong autodidact though, there are probably people who prefer getting dragged through things by homework.