Personally, I don't think that it's really a tradition - it's a combination of smooth canvas mats (which encouraged the practice) and young students (whose knees could hold up to the training) after the war.
The young guys on smooth mats introduced a lot more movement than existed previously. If you look at Daito-ryu and other traditional schools there was very little of the moving around on your knees that you see in Aikido today.
Yasuo Kobayashi used to say that he was the one who introduced shikko as an exercise - in the 1950's.
People today are paying the price with their knees.
What about in the days of the samurai and the 'inner sanctoms' of the shogun or 'boss'. Isn't that where it originated? In other words it had an original purpose and was practiced. I also have seen Ueshiba doing plenty. Thus it has a history all of it's own and a reason. Seeing the reason is seeing the use. Swordsmen I am sure would sit seiza for a reason to do with these type of movements too.