Honestly? Because recipe writers have a sense of humor—or a grudge against people who don’t own a full set of measuring cups. They’ll say “two 2/3 cups” instead of “1 1/3 cups” just to keep you on your toes. Classic move.
In reality, it’s often about volume scaling. If you’re doubling a recipe that calls for 2/3 cup of something, you get two of them. It’s easier to write “two 2/3 cups” than “1.3333 cups.” But hey, that’s why we have calculators, right?