Oh I could definitely write paragraphs criticizing that movie too. I enjoy it, but it's very flawed.
Anyway, is the problem shadows and fire regardless of whether it's anime themed? This makes more sense if you're just banning all fire and shadow themed martial stuff, anime themed or otherwise. Similar to how people don't want gunpowder, whether it relates to gunslinger Western tropes or swashbuckling tropes, but banning only one would likely be incoherent. However, right now ToB seems to be occupying this weird place where people are saying they don't want the anime fire and shadows (and perhaps more elements, but I'll stick with fire and shadows as being all inclusive for the sake of argument), even though, pages into this thread, and in countless prior threads, nobody has ever laid out anything anything resembling a convincing case that the fire and shadow stuff is intrinsically anime. You can find all of the same stuff in so many other fantasy genres that I find the anime accusations to be a fad that's long overdue for retirement.
I find it conspicuous you are not commenting on the other example I posted that contains nothing supernatural (Mountain vs Oberyn). Also, the warblade is described in the classes chapter intro as lacking supernatural powers.
Edit: if necessary I may have to troll for such flamboyant fight scenes from older Zorro movies and the like, that were made before anime had any popularity in the rest of the world. Suffice to say, all of the flamboyant things you're deriding are not unique to anime. So, if you want to eliminate such flamboyant movements, do so. It's just not internally consistent if you only eliminate anime ones, because there's no such thing.