For me, I consider sanshin and kime to be the most important aspects of kata. If you don't have the proper attitude and focus all the muscle memory is for naught. You have to blend them as you learn, not learn one seperate from the other. If you practice a kata 5000 times you're muscle memory will be well developed. You could mechanically go through the kata perfectly and still fail your test because you weren't really "there". For me though, it doesn't work well as a training aid. I think the ideals of kata are good to persue but imagination has to be used for imaginary opponents and how effectively you can use your imagination as a training tool will dictate how closely you can make yourself feel like it's the real thing which will, in turn, be a strong factor in how well you can cultivate your attitude and how realistic your focus will be. So I think some have an easier time getting more out of their kata than others. It's a good tool for learning how one move progresses to the next, developing finesse and the bunkai shows the theory and application. It's a neat little package, I just don't get as much out of it.
As for kiai, it isn't a yell, it's forcing the air from your guts really hard ("OS!", not "EEEAI!") to tense the body at the precise moment just before impact where it will be most effective. Like an uraken/backfist, you don't tense it up until just before you make contact. When you exhale (not kiai) with a less dynamic technique, you aren't letting much air out, the idea is that the air coming out gets "pinched off" which creates pressure in the body, like a steam engine, and contracts more muscles in the body (remember, you don't hit them with your hands, they're just levers that make contact, you're hitting them with your body) again at the point of impact. A kiai is just a bigger exhale, theoretically giving you even more power. Many feel unsatisfied with the amount of sound they can make exhaling and embellish it with their vocal chords more. I don't think that's necessarily a bad thing.
Personally I think a really loud crazy yell is more effective on their psychology. Just make sounds like one of those aliens from "Mars Attacks" while you beat on him. "Aht! Ahtadat! AHT!"
Really though, we knew this vicious dog up the block who was always jumping on the chain wanting to get a piece of me, and I assume, most people who walked by. My mother and I were riding bikes home one night and we recognized he was the dog, out roaming off his leash (and it was dark, he was already within 20 feet of us before we saw him). He ran toward my mom and she let out an immense scream of terror that caused the dog to tuck his tail and trot away with his head down. I don't blame him, never heard anything like it either. The effect sounds can have on psychology is immense. They can have a distracting effect, they can freeze you up or they can even get you to hit harder because you think you're hitting harder.
All in all I agree with Xue though and that the CMA schools of thought have very valid ideas on the subject. I do believe it has a physical effect on helping the body hit harder but more than that the psychological effect of knowing what it's for when you use it. Psychosomatic reinforcement or something like that. Many theories are valid and there's no perfect chess game. Always a foil for everything.