The late Saito Morihiro Sensei used to explain shihonage and kotegaeshi with the sword.
In the clip (0.00 - 0.40) you find his usual display of shihonage's principle of being able to throw someone in 4 directions (and therefore 8, 16, 32... ad infinitum).
Coincidentally Daito Ryu has the same throw but call it gohonage (5 directional throw) where the directions are north, south, east, west, and the added direction of "on the spot - i.e. where they (or you) are standing)".
For me it is also about training how to move freely in any direction as the situation demands it.