Yes, Hawaii has a quarantine program, so carrying them on wouldn't be allowed because then you could easily bypass the quarantine.

So that's a bad example, but you make a valid point nonetheless. Animals allowed in cabins really shouldn't go away, as its useful to those of us who have them, but I could see designated no-animal flights. It would, of course, be one more variable to track, and that does create extra work. And I'm not sure you'd ever be able to exclude service dogs (seeing eye, etc.)