So, some follow-up questions which I can't quite ask easily in a poll...
How is katatedori different than, say, the opening movement in shihonage to you?
If katatedori were part of a "combination" attack (ie katatedori mentsuki (same side grab, punch to the face with the other hand)), what physical effect would the katatedori have? Is it just a restraint?
If katatedori is just an exercise for beginning students to grasp the basics of things like maai and timing, why do we spend so much time on it in pretty much every aikido dojo?
Lastly, just an anecdote. Training with my teacher in the tenkan exercise (also known as "tai no henko"), I've been taken down, my face nearly getting planted into the ground, from a simple katatedori...