I don't know about the historical significance (if any) of the kind of differences that you've seen, but I'll just say that at least here in the United States, I've been exposed to pretty much all combinations of hanmi relationship (ie ending up in aihanmi or gyakuhanmi) and which hand to strike with (ie striking with the "back" hand by stepping through, striking with the "front" hand with just a shuffle-step).
This has been my experience also. Perhaps we would need to study the Noma Dojo photo archive to see more clearly what was done before the war.
I have just come back from a very interesting trip to Malaysia and Brunei, where they appear to start from the back foot. I suspect this was a convention established for the purposes of teaching maai etc, since no swordwork has been officially taught in the dojos I visited. I myself have been brought up on the kumi-tachi model (as seen in the early Saito volumes), where everything starts from ai-hanmi.
However, technicians like Seigo Yamaguchi were in shizentai and could happily move from either foot...
Best regards to all,