I agree that a disciplinary shaming, on top of a failing grade for the missing work, is harsh. The poor grade would be the logical consequence, and logical consequences tend to be the most effective.
I've been involved in education in one way or another for most of my adult life, and I feel real despair for children and families when I hear how much homework some schools assign elementary-age children. There is NO RESEARCH that shows this work actually benefits children before high school, and many developmental specialists believe its actually detrimental. There are also schools with outstanding educational records that do not assign homework.
I'm not sure what I'd do if I were in your shoes, but I may get a chance to find out, because my grandson will be starting K next fall, and I don't know what the homework policies will be at his school. In his case, I think he'll groove on doing "big-kid" work up to a point, but not all children are so academically-oriented, nor should they be expected to be. If the burden were to become onerous, I expect I would join with my daughter and son-in-law, talk to his teacher, talk to the school administration if his teacher can't make adjustments, and ask for a change in homework policy.
I've worked inside the school system, and know this can be somewhat risky, making your child a possible target for teacher or administration resentment.
On the other hand, teachers sometimes are forced to go along with ill-advised policies and are incredibly grateful when parents speak up, especially if it's an organized group of parents arguing for a change. So I'd do my best to connect with other parents concerned about homework, too, and present a united and reasonable front. I stress "reasonable," because hysterical or enraged parents get dismissed pretty quickly.
Do your own homework. There's lots to research on the web, and some well-written books on the subject. Here's one good starting point; a talk at this link by Alfie Kohn, a very thoughtful educator. ttp://www.alfiekohn.org/books/hm.htm