It's been already mentioned, BUT...
The reason on the Thai style round kicks are used is because those are the ones less risky. Everything else, especially kicks using the FEET as a striking surface, are simply not going to work as effectively, particularly when takedowns are allowed. You'd have seen them in MMA BY NOW if this wasn't the case.
Kicking in MMA takes an incredible amount of skill to do correctly and not get taken down. This means that you're going to have to throw those kicks in combination with good punching. That's going to be hard to do while using the feet as a striking surface. Kicking with the shin leaves you much closer to your opponent and able to throw that sort of kick after a combination of punching, from which you can "hide" the kick behind. Kicking with the feet requires more distance and is more clearly telegraphed.
While kicks can be powerful, kicking itself is often the weakest strategy. How many times have we seen guys attempt to kick and only get taken down for their efforts? Plus, many kicks tend to work primarily against bad, tired or injured fighters. For self-defense purposes, I'd say leave them in the dojo. And kicks while using the FEET? Forget about it.
Just my opinion.