For one, it's way too convenient that any Kryptonite landed on Earth to begin with. That it was found and discovered as Superman's weakness is also way too convenient. So adding in another rock that does the same thing but isn't Kryptonite, that's asking too much.
well there are more than one type of kryptonite
green K: fatal but only to kryptonians
red K: effects on kryptonians are unpredictable and temporary
gold K: permanently robs kryptonians of their powers (without killing them)
blue K: only deadly to bizzaros
white K: deadly to all plant life in the known universe