Good posts from Alec and Edwin imo.
Michael: Quick, stable, powerful, centred movement is a core principle of all Aikido - this is all that is necessary to deal with a shoot. Edwin gave one technical option. So I guess that knocks out your theory that it isn't taught in Aikido. If you need more clarification, google the words shizentai or mu gamae and see what you come up with. This is a central part of the core of Aikido's movement methodology, without this you have no structural foundation and everything else, no matter how pretty or "apparently" effective will fail. If you don't know how to stand properly, how can you know how to move properly?
What I am hearing from Michael is the same concept I alluded to earlier about the passive student. One must aim to see the principle behind the technique. it is often seen with students who can't handle a round punch even after having dealt with innumerable yokemen uchi attacks. They allow the change to take their centre instead of finding a way to adapt to the not so new pattern of movement.
In the end my post is about truly getting the most out of your training by deeply searching into the principles and not just sitting there, copying the sensei in "monkey see monkey do" manner and hoping that skill and understanding will come through osmosis or conduction.
As I also indicated in one of my earlier posts, this approach may not be for everyone as there are those who have no desire to actually evolve in their training but merely do it for exercise or some other value. There is nothing wrong with this, but it is important not to be delusional as to one's abilities at the same time. Again, this has nothing to do with self defence applicability, but honesty in one's understanding of Aikido and what one wants to achieve as a goal or final goal in that training.