My take on this isn't universal, I know, and I can't speak for others, but can explain how and why I "grade" homework - and a lot of homework. Caveat: My scale was always modest. More than about 30 students in a section of a course was unusual. I've gone as high as about 50, but that is probably the limit without help. I'll also note that for some huge classes (Harvard's CS50) the actual student/staff ratio is about 20/1, so even that is reasonable.
But there are two issues here that might be confused. Dan Romik alludes to this. There is the question of feedback on student work, which I consider absolutely essential to student learning. There is the separate issue of assigning points or such toward a final assessment (grade). So, even if I don't "grade" (assign points to) the homework, I still need to read it and comment when necessary - feedback.
There are a few reasons why I need to give feedback, especially, perhaps, in STEM courses. First, I'm not perfect. Second, the students aren't perfect. I may say something that gives the wrong impression and if it is missed by a student and not corrected, then they might get false "insights" that lead them to error. Learning requires practice and feedback. Practice without feedback can lead you to crankery. If the only assessment of a student's learning is at a final exam, then it is too late for them to make corrections in their learning.
It is also important to me that the students know where they are in terms of their final grade in a course. On any given day they should, ideally, know what their grade would be if the course ended that day. This has led me to adopt cumulative grading where each task has a number of points assigned (including tests) and students can know what percentage of the available points they have already "earned". If a course has 1000 points available for tasks, and 900 is the break for an A, then the student knows how far they are from that mark and how many opportunities there still are to achieve it.
For me, but maybe not for you, exams were a relatively small part of the overall grade, certainly less than 20%.
I also gave students the opportunity to re-do homework for which their earned point total didn't satisfy them. They couldn't get full marks for second tries, but could increase totals.
One advantage of this scheme is that I almost never got complaints about my grading. And my feedback on papers also gave some hints on how they can improve, even for a given assignment.
Oddly enough, I was perceived by students as being one of the "harder" or more strict professors. I had high expectations, but tried to enable all the students to achieve them. I was willing (and told students this) that they could all fail or they could all get full marks, depending on how they applied themselves. I had few failures. And luckily, I had a dean that would back me up.
Note that different students have different expectations for a course. If they are satisfied with a B grade then once they have achieved the required number of points for that, then additional points matter little. You can treat this as a feature or a bug, but being a few points short of the next grade can actually be a goad.
Also see: https://cseducators.stackexchange.com/q/4513/1293 and https://academia.stackexchange.com/a/112251/75368
I once had a math professor (much hated) that used a different plan in math courses. Instead of grading homework he would have "pop quizzes" at the start of nearly every class. We would spend the first ten minutes or so solving some problem from a recent lecture. These were graded. This was pretty much all "stick" and no "carrot", but at least we couldn't slack and our grade was spread over a large number of small assessments.