I have a theory, based soley on my gut feeling and nothing that could be considered even remotely scientific, that if I practiced nothing but kotegaeshi for a year my ikkyo, nikyo, sankyo, etc would all get better (assuming of course I already have some level of base profiency in the technique).
With all due respect, I don't think so. While techniques do have many common principles, they are different and those differences would take some adjustment. It's a bit like supposing that shooting three point shots will improve your lay-ups, or you'll never have to practice with a pitching wedge to get out of a sand trap in golf because, a golf swing is a golf swing --- in principle. So just hitting drives and putting will take care of it.
You can think of hundred of examples if you try...hitting a baseball vs bunting, hitting a forehand vs hitting a backhand in tennis and so on....
Ultimately, I suspect if one trained in one technique and only one technique for an entire year, their aikido would be terrible. It would be "dead". The aikidoist would forever be attempting to force a pattern onto the situation instead of blending with what is.