Alot of valid points have been made I believe that someday it will be used. What I mean back when the ufc first started jiu-jitsu (gracie) was the dominant martial art where no-one could defend against it. Now it is the turn of karate(machida/shotokan) to take over. Joe Rogan said it best in martial arts it is the goal to inflict as much damage possible without receiving damage. Aikido fits this perfectly avoiding confrontation at all costs. As for the comments saying about the staging in all demonstrations they are choreographed for the simple reason it is more enjoyable to watch.

Maybe some day a guy who has been training in Aikido since childhood will cross train and will try out MMA, but there are tons of reasons why Aikido is not the best MMA martial art.
Probably the dominant reason is that MMA fighters look to martial arts for effective skills that they can utilize in the Octagon. In MMA striking and grappling are both legal and fighting systems that focus on those skills make the most sense to train in. Most aikido techniques are illegal in the Octagon. Also, remember that UFC awards points for aggression, which Aikido is not best suited to.
Some Aikido principles ARE utilized in MMA though. Counterstrikers use the concept of safe distance and moving off the line of attack and I've seen tenchi-nage used by a couple of fighters. Apparently irime-nage is effective for throwing an opponent up against the cage.
At the end of the day Aikido isn't a competitive art, the subtle techniques take years, sometimes decades to master the effective use of in real life situations, MMA doesn't allow small-joint-manipulation, and Aikido philosophy is suppose to be non-confrontational.

yeah well... I don't want to be rude, but these nice Aikido demos are staged up...

In fact this demo (exercpt rfom the "Martial Art Festival" wich take place in france) is staged up.
I'm not arguing the fact that aikido is efective, but don't fantasm to much about it, you can see here, the action is well trainned and timed.
In reality the need years of trainning to really perform these techniques and they are not like in staged action or exhibition.
Anyway, of course you dn't have any lethal or dangerous techniques allowed in MMA, because the point is not to kill someone or disable him.
If you wanna do so, the A bomb is the finnest.
Imagine aikido or even karates, kung fus, penchak silat or krav maga techniques used in the cage could be unnapropried.
In fact MMA competition is about striking, and grappling, because there are not thinked to be lethal: knout out or submission.

To illustrate my point, see the real jujuutsu is not used.. only the katame waza is ued wich evolveld in Bjj. The nage part is more for aikido. Same for Judo...in judo for MMA the action take place on the ground ("ne waza") mostly because the techniques are about control and submision and not disable totaly your adversaire

Oh and I forgot about the rule in mma about not being allowed to do small joint manipulation/ breaking fingers which often sets up an aikido joint lock/throw

This is crappy demo Tissier aikido. Aikido hasn't been used in mma because you can't kick the groin, stick your fingers in the eyes, strike the back of the neck, attack one guy with a group of your friends or use weapons. If anyone used proper aikido in mma it wouldn't be entetaining for the crowd because the guy with the good chin using kickboxing standup with his groin wide open or the sport grappler/ankle biter would be killed in 2 seconds. If you had 2 aikido guys fight they would just stand there waiting for the other guy to attack and on the rare occasion that one actually would he would do it properly without any openings so all the defender could do would be to make him take a roll.

because in mma, fighters arent trying to punch an area 18 inches to the right or left of one's belly button, THEN pause with their arm hyperextended and head down until you grab something.

I wonder why aikido or its principles have never been utilised in MMA.