Kicking is actually a really bad fighting move unless you're the right build for it and using a discipline that emphasizes it. It tends to be slower, it takes you off your center of gravity and therefore makes you easier to topple, and in the hands (feet?) of the less experienced it's less accurate because our skeletons just didn't develop with kicks as a combat technique in mind, which also steps into the realm of not being able to fully project strength that way.
Kicking delivers a LOT of power but only in certain ways and angles, and the extra reach afforded by our very slightly longer legs isn't exactly an advantage.
In other words: kick 'em while they're down, definitely (you'll get good results), but otherwise try to avoid kicking if at all possible unless you're a master of a martial art that really prizes kicks.
Stick to punching. Your body is designed much more to favor that kind of movement so it's easier to aim and project most of your strength, preserves balance, and it's far easier to learn how to fight with your fists anyway.
And then bring a knife to a fistfight and a gun to a knife fight.
And then avoid fighting entirely if it can be helped.
Obviously, if you are a video game character, disregard everything I just wrote. Do whatever the hell you like, video game characters.