Hello Rick,
You have raised a question which is interesting to wonder about. Prohibiting students from taking a quiz, even if they are late, is this pedagogically adequate?
I teach young people at university and I personally wouldn't do that. It's easy to accommodate late students, especially with Moodle. Of course, they may have difficulty with punctuality, but I would let them do the quiz anyway.
I even think I would give them time to finish it, but that's just me. I may be too easygoing. Taking a quiz is part of the learning activities and, in my opinion, that is what matters first. I don't really care if a student is a little late.
On the other hand, I understand that other teachers can be stricter, and I believe that is good for the students as well. A little discipline, applied in the right way, can also help.