Well, I didn't know that shodaime comes first and then nidaime etc etc. I may sound reason my thoughts, but correcting them is welcome.
That post was not a reaction to your post anymore. In your case I just pointed out that your reasoning was essentially correct, only we already knew that there's a 1st sword. So this wasn't some speculation, implication or suggestion anymore. Instead of Ichidai though it was Shodai.
I don't know about making it needlessly complicated just a bit of devil's advocating and exploring any idea as far as I can.
Swords don't found anything but the Kitetsu school was and each blade was made by the succeeding class. You're probably right, I was just posing the possibility that it could be looked at as the first creator having made Shodai then his 1st generation of successors made ichidai and the 2nd generation of successors made nidai the third making sandai.
It's simple: three swords. One, two, three. Supreme sword, great sword, skillful sword. Then you make that into 'yeah actually you can interpret this also as founding, so we can shove an additional sword into this for no reason and that totally doesn't fit the pattern of the sword grading scale'.
You're not devil advocating if your reasoning is flawed and contradictory. The bare minimum for doing that is that your reasoning can't be immediately discarded even if it sounds stupid. In your case however your reasoning definitely doesn't fit. This is a fact, the Kitetsu-series was introduced as Shodai, Nidai and Sandai, respectively part of the Supreme, Great and Skillful Grade Swords and translated as 1st, 2nd and 3rd generation demon-cutter. If Shodai was meant to be "founding", then that means for some reason they jumped from founding to two and ignored one completely, this despite that they do remain conform with the sword grading scale? Then they should have been introduced as Ichidai, Nidai and Sandai, but if that had been done, then you can't reason Shodai = founding as it was never mentioned.
So the thing that made you come to this interpretation invalidates it at the same time. Also I'm not that familiar with the Japanese language, but when I checked some things ichidai means a generation or one generation. It doesn't provide any chronological foundation, while shodai very well does. Same thing with your school as the people who make the swords are a completely different thing than the swords itself.
So yeah this not a bit of devil advocating, this is just making things needlessly difficult as based on a very iffy translation interpretation you turned a very clear, simple and basic concept into something flawed and contradictory for no reason.