There are a few reasons why you don't see Side Kicks in MMA.
1) Kicking skills aren't as advanced in MMA. Just like in comparison to boxing, most MMA practitioner's kicking skils are not as advanced in comparison to those who kick consistently. Throwing a kick in such a fashion is not an entirely "intuitive" thing either. There is a reason why the side kick is the second taught kick in most TMA's and it is thrown hundreds of thousands of times over the course of study. Considering that, it is not a tool that can so readily be implemented into a MMAist's fight game. In that regard, Kin is correct.
2) It is a risky technique because it is harder to throw without being telegraphed. Unlike the MT style of throwing a round kick, you can't throw a side kick without the chamber. This is really hard to do without revealing your intentions, and if you consider the footwork involved with a sliding/stepping side kick it can it gets even harder.
The only way to get around that is to set up your side kick by way of combination (which I can gaurantee you that a very small percentage of modern MMAists even entertain the idea of training-see above) or by kicking at a high volume with multiple types of kicks. I've seen a few full contact Karate, TKD and Kick Boxing matches where side kick kos occur after the person has been peppered by round kicks in succession. After the person gets their opponent used to blocking the round kick, they chamber the leg and switch to a side kick catching them blocking the wrong way. This wouldn't happen in MMA with the option to clinch or take down the opponent. Which brings up the last point:
3) Side kicks require range, and can be stuffed regularly with a takedown. This is in relation to the both above. If you correlate the side kick to a rear cross/straight, then you see that the true "breaking power" of the kick is held at the end of the attack. If the contact is too close, then the practitioner ends up pushing their opponent away and not breaking the target. Consequently also, if the person defending the kick steps aside from it the momentum will carry them past the target unless it is quickly snapped or jabbed out from the front leg. Even then, the body turn and extension will leave the thrower on one leg with their body turned away from their opponent. That is a prime opportunity for a takedown.
Taking that into consideration, it's not too suprising why it isn't as prevalent in MMA. There are a lot of risks, and there isn't as much time for competitors to dedicate in order to make regular use of the skill when they have to concentrate on everything. In time, I'm pretty sure that we'll see it implemented by a competitor with effective results. Heck, they said the same thing with the turning/back side kick, the mongolian chop, and jumping attacks on a prone opponent but Sakuraba proved that all of those can be used with great success. It will happen.
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