I think old-skool aikido used the term "shite" and some style still do. If memory serves, the connotation of the term was one of designating a leadership role (leading/receiving, etc.). I think once you experience takemusu aikido, it becomes difficult to designate a static role in the paired relationship which causes all kinds of problems.
Waza is not kata.
I am not sure if changing semantics will help resolve what I feel to be a source of the problem. I think the confusion comes in when we think we are doing waza, but we are really doing kata. I would focus instead on more strongly identifying kata practice distinct from randori and managing an expectation of success that encourages more activity from uke.
I like your point about kata vs, waza AND IME, not many clubs clearly define the difference between the two.