I'm sure all those iai schools have their reasons for training drawing from seiza. Emphasis on training, as opposed to actually representing an actual situation that occurred (as in samurai in seiza with their katana still in their obi). It's not all from seiza though. There are iai schools with a sizable standing iai curriculum. Also, schools like Katori Shinto ryu have iai but none from seiza afaik.
Seiza wasn't really a thing until the Edo period...I've read that it was associated with the spread in popularity of tea ceremony. In the warring states period warriors sat on their butts with their legs folded when they were in polite company.
Not to put too fine a point on it, though, but:
This is not seiza, and it is not even the iai-goshi posture some iaido schools practice, this is hiza.
But I wouldn't give anybody crap for calling this kneeling.
Iaido made inroads into the west before pioneering Western practitioners got into koryu and spread knowledge to non-Japanese language communities, and there was this very scathing rebuttal of claims by iaido practitioners to be practicing "authentic samurai swordsmanship" that reverberates a bit to this day. A warrior sitting in seiza with a long sword is not a real combat situation, seiza is not a combative posture, iai goshi (one leg under the butt, one out to the side) is not a combative posture, Zen was not popular among warriors until there wasn't much war, the Edo period saw a widespread, general degredation of combat skill and efficacy of training methods and arts founded in that period are "flowery swordplay," etc.
I figure it's just because the needs of society changed and the warrior culture changed with them. At some point these guys decided they should spend a lot of time practicing drawing their swords from seiza as a way of organizing and developing their spirit.
To get back somewhat to the original thread...in iaido there is not as much moving around in seiza as in Aikido suwariwaza. Nor koryu for that matter.
But there are a lot of movements and postures that would be considered orthopedically verboten these days. Lots of moving into and out of very low postures with knee advanced way out past the toes, lots of bending the knees to lower the center, while keeping the back very straight. Sitting with the butt completely on one or both heels, and then exploding to a standing position. I generally maintain the view that koryu arts expected a degree of flexibility and strength in the legs that seems much less common in modern non-Japanese than in modern Japanese.