I had (and still have) lots o' trouble with ude kime nage. I believe that our current ude kime nage (and other kokyu nage throws such as kaiten nage) were altered by O'Sensei and subsequent shihan to be more safe to practice. Largely, my proof of these altered techniques lies in the outward expression of ukemi. That is, we do not direct our opponent into the ground [as directly]; we throw our opponent away with a clear path of ukemi. I believe this altered ending is inconsistent with some of the older jujitsu arts where nage focused tori's energy into the ground. In Judo we call this "dashing" and the reference is to place tori's shoulders close to your feet.
The several references to a Judo-like application of this technique often put back into the technique the "dashing" component. The arm bar holds uke close to nage; both a foot sweep that removes the balance structure and the top-heavy shoulder pressure drives uke into the ground. If uke avoids the foot sweep and escapes he leaves beyond a balance void (shikaku) from the extra step. I think ude kime nage in aikido is representative of these principles without the danger of the fall. Try any of the related Judo applications and I think you get a different result, compliant uke or not.
But that's not aikido, right?
To get more technical, I think a big part that we miss is the irrimi component of the throw. When I thought about ude kime nage as a throw I always entered too shallow. I am moving to get behind my attacker, then turning to deliver my counter-attack. My partner needs to feel my energy/intent behind her and recognize the inherent danger in my position. She should be abandoning her position in conjunction with me applying pressure, the result is her balance broken forward. The irrimi is the cause of kuzushi and why I am able to move through her shoulder without opposition. Also, I think we sometimes move our inside leg too soon. when I enter, I move with a tenkai but I do not step through the throw until I have started her movement. If I move my leg through the throw too soon I find that I give her a balance structure and lose kuzushi.
My opinion on ude kime nage is that it was modified and you need a little work to get back some of the functioning jutsu. I do not think that is a bad thing but it does mean you need to be sensitive to the potential of what nage could
be doing to you. I turned to judo to find some of the functional aspects of ude kime nage and there is no shortage of techniques that clinch tori's arm while removing the lower balance structure - they just don't give tori a nice projected exist strategy.