As someone who used to be a big kicker, who's coming off of a 4-month stint where I trained nothing but my hands, my opinion is a resounding 'HELL YES!'
As others have mentioned, kicks are very damaging, have longer reach than punches, and give your attack a little bit more variety. Even more important than those very worthy examples of the importance of kicks is the fact that their inclusion changes the range of the fight. Without kicks, the neutral ground/no man's land is just beyond jabbing range. That is where you are safe to feint and play with the distance, and it is from there that your attack will be mounted.
When kicks are in play, however, the outskirts of jabbing range is no longer a safe zone. Coming back from a stint of boxing-exclusive training, that was really tough to cope with. I'd habitually look for that range to play in, but that was to my detriment for two reasons...
First, whenever I'd settle there, I was within my opponent's reach in terms of kicks. Action is faster than reaction, so having space between you and your opponent can give you that extra milisecond you need to react. When I would sit contently within kicking range, I was constantly getting pelted in the legs while I was trying to find my range with a jab.
Second, because my opponent is wary of kicks (even though I wasn't throwing them often), he would look to establish himself at the edge of kicking range. So whenever I would try to set up camp at the edge of jabbing distance, he would already be on his bike -- rightfully perceiving my narrowing of the distance between us as a threat.
TLDR: He would never let me settle into the range I needed to get off punches/I would chill within perfect reach of his kicks, hence be a sitting duck. Kicking changes the range of the game, and if you don't kick, you're much more limited not only in the angles and heights of your assault, but also in your distancing. Furthermore, you automatically concede the kicking range to your opponent, making it that much easier for him to control the fight.
Highly opinionated but out of touch with the current MMA scene.
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