You do realize that there's nothing in Aikido that's not seen in other styles?
What makes Aikido distinct from other styles is its philosophy - something very compatible with police forces around the world (except for those in totalitarian regimes where the police fear no one).
Therefore, the only videos you're gonna see of anyone doing any martial arts is going to be someone doing something common to all martial arts.
On the other hand, I agree with you: it doesn't work in real fights, mma competitions, or even in the dojo. It doesn't work any more than a recipe has taste or a house blueprint can stand up to a hurricane. What we are taught in martial arts - including Aikido - is techniques. Until they are taught to a human being, they are abstract. The human being has to make the techniques come to life.
So technically... you're right: it won't hold up in fights, etc.
Having said that, there are two reasons why it (or rather the practitioner's skill) won't work in MMA competitions. First, because it's the wrong tool for the job. Aikido works on a philosophy of avoidance. Imagine Silva walking out of a fight because he doesn't think that fighting's the answer! Second, Aikido is the wrong tool, because many of its techniques involve small-joint manipulation - a stated prohibited rule in MMA. Don't blame Aikido for this... Ask Dana White why he has this rule in place.
As to real fights... you want to know why you don't see Aikido being used in real life? I mentioned before about its philosophy of avoidance. Apparently, the absence of the videos suggest... it's working. There, I think, is your proof.