A while back I asked a similar question and got not much of a reply. I wanted to know where the idea to train irimi and tenkan (2+2=4 techniques etc) came from. If you look at old vids of Ueshiba he does not seem to do this (maybe there are some I have not seen??). Does no one know who introduced this or why we do this? I think there was a reference to Kishomaru Ueshiba but even if so, why? If we cannot answer such simple questions ... Personally, I now think this (repeated irimi and tenkan) to be useful, but also limiting. (Tomiki do not train this way, Yoshinkan do in part, ... some do ... some don't etc.).
Slightly veering to the right of the conversation, and I can't answer the origin element of your question, I'd like to comment on an advantage of the 2+2 training formula.
It evens out our brain and retrains it in a way that doesn't happen anywhere else. Same activity, same number.....different hands and sides. That's the catcher. The different hand same activity part. This, in other contexts, has been shown to release trauma from the brain and to re-route neural pathways. This may suggest that the use of our bodies in this way could re-train 'natural/neural' reponses. Perhaps even facilitate flow on both sides of the mind. In which case our system enters into a certain 'agreement' with itself. Now that's a technique.
I would also be curious to know who improvised/introduced this formula.