That fix sounds logical. It would be like sending a cat to a professional groomer to solve the problem. I think I know why EA avoided giving the wash cat option: cats have a high chance of becoming ill or traumatized by the experience. IRL, compared to dogs, cats are a lot less tolerant to shampoos, conditioners and such treatments, so a person really has to check the labels carefully to make sure they don't make the cat sick. Never give a cat a flea dip to get rid of fleas: that can make them deathly ill. Then there is of course the chance of the experience causing the cat to experience trauma. That is a lot of stuff to consider, so to keep the game play simple, play it safe and avoid possible backlash from cat enthusiasts, they likely just left out the bathe cat option.
Frankly, though... I'd like the option to hire a gardener that can go hack down the offensive bush that represents "a skunk" or a "rabid squirrel".