Granted, I play more with cats than with dogs, so I get to use litter boxes. I always spring for the expensive one with lasers so that I don't have to clean the litter box. Not just because I'm worried I'll forget, but because I hate doing it. (Irl as well as in game) I'm not as bothered by it as you are, but that doesn't mean it's a feature I like.
There's also a mod out there for an "outdoor" litterbox that's two rocks that never needs cleaning, if you're not adverse to mods.
So that's a solution for cats. I don't have one for dogs, unfortunately. Wish I did, I might have more sim families have dogs as pets.