The statement about "crude power and endurance" iis an inaccurate generalization. It depends on the fighter. And there are many MMA fighters who've trained in Kempo (Chuck Liddell), Shotokan (Lyoto Machida), TKD (Stephan Bonnar, Anderson Silva, David Loiseau) and Muay Thai (Wanderlei Silva, Forrest Griffin, Spencer Fisher), not to mention boxing (Quinton Jackson, Marcus Davis, Nate Diaz).
There strikes would be no more accurate and their technique would be no more supperior, all things being equal. The reason is that in a real fight, adrenaline starts going and you start to realize that you, too, could get punched in the face. Someone trained in the "traditional" arts you mentioned would have to go through similar training to the MMA fighters I listed above to even stand a chance, because that's how you get used to the stress of a real fight. You train like an MMA fighter.
So final answer, could they defeat an MMA fighter? Sure. But because, all other things being equal, a well-trained "traditional" martial artist would be on par with an MMA fighter, at least at striking. All fights start on the feet, so they'd stand a chance. Let's call it 50/50 'til it hit the ground.
Edit: You're wrong about most UFC fights ending up on the ground. It depends on the fighters involved, but I think the majority stay standing. All of Liddell's fights in the past five years have stayed on the feet until someone got knocked out. Jackson-Griffin was almost entirely on the feet. Most of Spencer Fisher's and Jens Pulver's matches stay on the feet. Machida stays on the feet unless his opponent has no ground game. Both Anderson and Wanderlei Silva keep most of their fights upright. Rich Franklin prefers to stand and punch. I could go on but the point is that MMA is about taking the fight where you're strongest or where your opponent is weakest. For someone with the power and accuracy of Liddell, that means the fight stays on the feet. For Couture, who has better wrestling than most of the MMA world, that means the fight goes to the ground. So no, they don't take it to the ground because they CAN'T stand up, they take it there because a) they're a superior ground fighter or b) they're losing the stand up. Just how much MMA have you seen?
Edit 2: No, having really great kicking is not the answer. Kicking leaves you vulnerable and off-balance. And there are already very good kickers in MMA. Have you seen Thiago Alves, Mirko Crocop, Cung Le, Anderson Silva, Bas Rutten, Guy Mezger, Gregard Mousasi, Wanderlei Silva, Keith Jardine, Yves Edwards, Georges St-Pierre, "Shogun" Rua, Jean Silva, or David Loiseau? Rich Franklin and Forrest Griffin have won recent fights due to their kicking skills. And even Kazushi Sakuraba, known mostly for his grappling abilities, could throw one hard kick. Crocop's patented Left Head Kick was the most dangerous one-shot weapon this side of a .44 Magnum. The fact that you don't know this makes me, again, question how well you actually understand MMA. But let's look at some strikers who've crossed over:
Semmy Schilt: his background is actually in Karate. He started fighting in MMA in Pancrase and for the first three years of his career he regularly lost to smaller fighters. As his grappling got better, he started to win more. The only guys who have beaten him since then are among the best in the MMA world. His striking is good enough to have earned him six K-1 titles with wins against Michael McDonald, Remy Bonjasky, Jerome Le Banner and Ernesto Hoost.
Mirko Crocop: he actually had much more success in MMA than he did as a kickboxer. His kicks are definitely part of this, but so is his ability to sprawl and defend himself from his back. Still didn't keep him from getting knocked out by a wrestler...
Mark Hunt: he's run hot and cold in K-1, but was their 2001 Grand Priz champion, having beaten Jerome Le Banner, Stefan Leko and Francisco Filho to win it. In MMA he's 50/50, with questionable wins and surprising losses.
Jerome Le Banner: one of the best kickboxers in modern history, he's past his prime now but still sports an incredible 74-16-1 record in K-1. His MMA record is 3-1-1, but the only guys he's beaten were nobodies.
Cung Le: he's an incredible striker, but I'm not sure how much you'd count him since he's got a solid wrestling background as well. He's undefeated at San Shou, although in fairness he's the only guy in the US who really practices it. He's 6-0 in MMA, but the only win worth noting is one on an over-the-hill Frank Shamrock, who hasn't been relavent to MMA since 1999 or so. He's pretty crowd-pleasing, but he hasn't faced any real competition yet. And, as I mentioned before, he's a very good wrestler, which helps him keep his feet.
Speaking of Cung Le, let's address this "Jack of All Trades" myth. Le has very technical kicks and takedowns. He learned those in two different disciplines. Georges St-Pierre has Olympic-quallity wrestling, world-class boxing, and has beaten good fighters with submissions, again things that he learned in different disciplines. Other fighters, like Fedor Emelianenko, BJ Penn, Miguel Torres, Jens Pulver, Rogerio Nogueira, Andrei Arlovski, Gregard Mousasi, John Jones, Stephan Bonnar, Marcus Davis, Kid Yamamoto, Genki Sudo, Josh Koscheck, Wanderlei Silva, and Dan Henderson have developed excellent skills in two or more areas. The best MMA fighters have professional-level boxing and kickboxing, Olympic-level wrestling or judo, and world-champion level grappling and BJJ. I think you need to watch more MMA to understand what you're talking about.
Sigh... Edit 3: I get that you're not attacking MMA, but you still don't know what you're talking about. The fact that you're suggesting that jumping kicks don't leave you vulnerable just reenforces that. I've been throwing kicks practially all my life. I've had some good teachers, including an Olympic alternate in TKD. When it comes to the use of kicks in general, and their use in the totality of the fight, I know what I'm talking about. In fact, according to your theory that you need 8 years of study for proficiency, then I am much more quallified to talk about karate than I am MMA. I didn't come from some three-year school. Took me about twice that time. So listen up:
Side kicks- I use them in MMA sparring. They work. However, as with all kicks, they leave you vulnerable because you are compromising your base. These in particular are hard to work into combinations because your opponent is at the very limit of your range.
Back kicks- if you're talking about spinning back kicks, I use them when the opponent has moved out of range due to a roundhouse kick. The range for them is quite wide. Anyone who throws them by simply turning their back on their opponent is foolish. You should never expose your back.
Hooking kicks- these have very little utility. They are only good for head kicks and as such compromise your base more than other kicks. They also, by nature, do not have the same power as other kicks. So to summarize, these are low-powered, high-risk kicks. Using them in a setting where one can be taken down is foolhardy at best.
Crecent kicks- are you serious? These are huge, swinging kicks that position your hips perfectly for you to be taken down. Probably the most useless kick in the history of kicks.
Double kicks- trying these in an environment where you can be taken down is about as smart as installing a screen door on a submarine. You're going to get taken down.
You see the roundhouse kick the most because it is the most utilitarian kick in use. It's appropriate for striking head to toe, can easily fit itself in with punching combinations, is quicker than most other kicks, and because it comes from the outside of a target it puts itself in a position that's easier to defend if (when) it gets caught.
Now tell me, if kicks were so deadly, how come no traditional martial arts, and I mean the ones genuinely over 100 years old, advocated using their use above the waist? Check out the Bubishi and tell me how many kicks you see. How come we don't see death after death in Muay Thai, full-contact karate, Taekwondo, and kickboxing competitions? You are severely overestimating the power of kicks. Yes, they stand a better chance of finishing a fight, but they are no where near as lethal as you imagine. Son, I've been training in martial arts for 23 years, most of it in so-called "traditional" systems. I've probably been throwing kicks longer than you've been alive. I know what I'm talking about.
Edit 4-Over 60% of takedowns are in the clinch. Kicking leaves you one one leg. Multiple kicks leave you vulnerable longer. If you trained full-contact you'd know this. You have no evidence that kicks are "lethal". How many deaths are in Taekwondo, karate, Savate, Muay Thai, kickboxing, and San Shou competitons? You're just guessing without any proof.