If you look at some of Ikeda Sensei's demonstrations, you'll see that he makes sure that he has a good connection. Sometimes the connection can be a little iffy and solid in such a narrow direction that the availability of controls is limited. That's when an overly-cooperative Uke can pay off, but the theory should be pretty obvious: make a unit connection; move the combined unit with your middle. That's what Ikeda Sensei keeps saying (he's said it for years, from what I've heard), although granted some of these things are subtle enough that you need someone to show you the first steps in a careful and expanded way.
I am grateful that I have had Ikeda Sensei himself show me these first steps (along with my own Phong Sensei and several others) because I never would have seen them just by watching demonstrations. I am simply not that bright or observant.
The only time any of the instructors I have had used anything near a cooperative uke was in instruction trying to get us to see/feel these subtle connections and extensions. Many would get frustrated if you did not give an honest and genuine effort.
There was always connection (maintaining your alignment and structure while taking their balance) and turning their center with your center. These seem to be pretty basic instructions in Aikido, but I seldom see them mindfully practiced and applied.