I definitely see your point, but all things being equal, why can't a karate practitioner simply out maneuver a grappler and punch and kick them into submission? I mean, there's a difference between rules that completely eliminate your ability to fight (like a grappler not being allowed to grapple), but what rules limit a Karate or Kung Fu practitioner from beating the crap out of an opponent with footwork, kicks, and punches?
Part of it is training, I think. Not many Karate or Kung Fu practitioners have practiced avoiding takedowns and grapplers, and it would take quite a bit of training and familiarity with grappling to learn to do so in a UFC setting. Most people just accept grappling, and counter grappling with grappling, as opposed to learning to avoid the ground.
The other thing is that the rulesets still favor grappling and takedowns iin comparison to many TMA contexts. Striking is somewhat handicapped, or at least changed by the use of gloves, and rulesets are actually more strict than people give them credit. Some of the obvious and very vulnerable and accessible targets, such as the neck, are completely off-limits -- the significance of which, I believe, anyone who hasn't trained in a TMA with open hands will not appreciate. You can't do things like kick downed opponents, and even the ring itself is designed to allow practitioners to drop to their knees without injury.
But the greatest difference, I think, is the fact that Traditional Martial Arts tend to deal more with "earnest" fighting, whereas sporting competition is much more of a "game" -- or, at least, the "game" is different in either case. Traditional Martial Arts
tend to deal with committed attacks against an opponent who is truly trying to get in your space quickly and hurt you. Your attacker does not have time to feel you out, and he has to decisively engage you or else you can simply walk or run away, or perhaps even draw or grab a weapon in the case of unarmed fighting. Therefore, he can't be too cautious about attacking you -- he doesn't have time to play games and feint and poke at you from a distance. He's never seen you before. He's never fought you before. He doesn't even know if you're trained or not, or if so, what kind of training you have. He doesn't know if you will fight back or just try to run away. He may have a weapon, or he may not; he may have freinds, or he may not; he may be engaging you in an alley, on pavement, on a dirt road, or indoors; there may be sticks, pipes, bottles, chairs, rocks, and other implements laying about that you or he could grab. All of this impacts the way he will approach the engagement, and the way you will respond to it. The same contrasts could be made for a battlefield context, or a beimo context, or any other form of combat. Traditional Martial Arts are an answer to these specific contexts just as sportive martial arts are an answer to sportive contexts. The intention of the combatants, and context of the combat, are different in each case. It's not a surprise, therefore, that sportive systems tend to excel in sportive environments.
It is also a matter of training, as some have mentioned. If you want to be a successful UFC fighter, are you going to do all of the extra work that is required to make a TMA work in the ring, or are you just going to go with proven methods that will yield more success in less time? If you care about winning, which you probably do, you'll go with the latter, and stick to conventional method. Competition, in this case, cuts down on diversity and ingenuity to some extent (or rather, I should say, focuses it along a narrow path), as it leads to very serious specialization.
At least, that is my perspective. But I'll add the usual caveat that I may not know what the hell I'm talking about
