My take on this is that there is a difference between demonstrating Aikido and demonstrating aiki on an uke - demonstrating aiki on an uke is one of a number of things you might do when demonstrating Aikido.
This is because of two reasons:
1) there are a whole raft of things you would want to show students that don't have to do with aiki. Or "IP" for that matter. Particularly if you are trying to train some martial skill into your students or yourself. Sometimes you just need to figure out how to properly attack a joint, for example.
2) Secondly, I have lately been thinking that the typical big, flowing Aikido movements come from demonstrations of "externalized" internal movements. Anybody who has trained with Hiroshi Ikeda Sensei should know exactly what I am talking about. You could look at some demonstrations of Aikido as being an explanation or picture of aiki, but without actually being aiki themselves.
I tend to agree with you. A good example of keeping things separate may be the famous conversion of the sumo player, Tenryu. Although familiar with sumo, most accounts indicate that O Sensei did not play sumo with Tenryu, but rather showed him aiki. Why did O Sensei abstain from showing aiki through sumo? While the converse of your example, I think an interesting example of the advantage being able to separate technique from aiki.
Yes, I think some of our waza distortion comes from deliberate exaggerations of internal movement. I'm not sold on the argument that external movement can demonstrate internal movement; I think at best it simulates a feeling that we try to emulate when training internals. I think this has been part of Sensei's struggle to communicate that instruction.