YetAnother,
Interesting question.
We (primary) revised our homework policy quite recently, to focus only on the things that we really believed made a difference - daily reading, learning of times tables, in higher years routine arithmetical calculations for the 4 operations. We did end up adding spelling + 'write a sentence using your spelling words' homework, tbh much more because parents reviewing the policy demanded it rather than because we felt that method of practising spelling made a huge difference to in-school everyday spelling.
In terms of book marking, again in primary, in my experience it is normal for every teacher to be expected to mark every book in between lessons in the same subject (so daily for Maths / English, maybe 1x a week science, 2x per week history / geography etc).
I don't know whether this is 'over assessment' - again, in primary in my experience it is normal to be asked for the following lesson / activity, especially in English and Maths, to in some way respond to how the children performed in the previous lesson. So for example, if when marking I notice a specific difficulty, or specific children achieving very highly, then I am expected to show how I respond to that with e.g. specific teaching of an area of difficulty, or further extension for those who have achieved well and are secure.
I don't know how that 'feedback loop' - at its simplest, teach, do, mark, adjust teaching - would work without the marking step. I know that a full 'circle all errors with red pen' is not necessary in order to be able to assess how a child has done, and what the next steps for the next lesson are, but equally NOT marking at all might, in a class of 32, mean that I might miss some children who were achieving well / poorly.
Obviously, not every lesson has a written outcome - photos, drawings, objects, discussions, videos, various electronic forms are also frequent lesson outcomes, and so there will be days when the 'traditional' marking is lower.
I suppose it depends on the purpose of marking. It seems to me it has two - to communicate to the producer of the work how well they are doing, and what they might need to do to improve, and, via the simple process of reviewing work, to communicate to the teacher how the pupil is doing and what their next steps are. All marking approaches balance those things: I can achieve the second simply be looking at the books in many cases, but that doesn't meet the first purpose, of communicating to the student, at all...