As mentioned in the OP, I have my own theories on the subject, and being a teacher, I also practice what I preach. So here is my take on the matter:
1. Homework teaches the pupils to work independently and to regulate their schedule. These are valuable skills which will come in handy later on and not teaching them this would be a disservice.
2. Homework should only be used for either repetition of material that has already been dealt with in class or for assignments that the pupils are capable of handling on their own.
3. Homework should almost always be limited to a 30-60 minute workload. Exceptions can for instance be special projects that the class is working on that sometimes take up more time than what is available in class. Kids need time to play as well.
4. The assigned homework must be adapted to the level of the pupil(s) in question, meaning that if you have a pupil in your class that is already struggling with the subject you must tailor the homework to his or her capabilities. The same goes for pupils who are ahead of the class average, although this is usually easier.
5. Homework should have a clear relevance to previous and later classes. This means that it is not always necessary to check and correct the homework of each and every pupil (although this should of course be done on a regular basis), but that the homework must be tied in with the classes at school.
So, for me this is a tentative 'yes', but as you can see, with some conditions attached.