I don't really get how these threads get very long when the answer is pretty simple.
There are things you can get away with in MMA that you just can't get away with in Kickboxing or Muay Thai.
The distance you can fight with a long, bladed stance is perfect for MMA where you want to stay farther away from your opponent you wants to grab you and take you down. People also simply don't train leg kicks that much, and if they throw them willy nilly, even a guy like Thompson can catch them and take you down.
You try that shit in a Kickboxing ring, you can get abused. Much like how if you fight in a Thai stance in boxing you will get beaten, and vise versa, there are things that are great in MMA that just don't working in other striking arts. If you go in with a Karate side stance in Muay Thai, you will be creamed.