Thanks a lot for your answers. In fact I was wondering why we use different types of kens. You could imagine different types of shinai in Kendo? Perhaps one answer is that Aikido is not a competitive martial art. All the fencing swords or foils have exact the same shape, length and weight (and perhaps alloy) eliminating any possible advantage which could occur from this. I understand that in Aikido the weight of the ken could varies a lot due to the wood essence, but the differences from the "Iwama bokken" and the "Daito bokken" are quite big. I tried one day to practice suburi with a Daito bokken and the filling was... odd. Practicing kumitachi with two types of sword is probably even more strange. Of course, nobody will do this in his dojo if he is not insane.
My point is: why we (different Aikido schools) could agree (to a point) on taijutsu and aikijo, but not on aikiken?