I don't know about US grading schemes, but here in Australia, pretty much every course has some form of assignments or series thereof. The assignments can be a small or substantial part of the final mark, or even the total final mark, depending on the kind of course.

I suspect the same is true in US tertiary institutions, and that railing against exams is just a tired old trope. It's hard to believe that it would be the general standard in the US to have the entirety of the final mark attributable to exams. But, like I said, I'm not familiar with their curricula.

My experience is from SUNY Stony Brook (a university run by the state of New York). What goes into the grade, is pretty much entirely up to the professor. I have had very few classes where the whole of the grade was an exam; but there were a few. More often, the homework is some portion of the grade, but it could be minimal (e.g., 10%). For computer science classes and some humanities classes, it was more likely there would be larger projects or term papers. For things like math, the homework was usually a smaller part of the grade. The real advantage of doing the assignments was that you could practice for what would potentially be on the test, and there would be a TA to grade it and give you feedback.