There's a bit of history here which puts this in perspective. In 1987, mangaka Kawahara Masatoshi first published Shura no Mon. This is a pretty standard martial arts manga in terms of setting and characters. It primarily follows a single character, Mutsu Tsukumoto. He practices a martial art Mutsu Enmei Ryuu. This martial arts style has apparently never been defeated in its 1000 year history. Shura no Mon ran for 31 volumes and finished publication in 1996. It does have a sequel which began in 2010. It was never adapted as an anime.
In 1989, Kawahara began publishing a prequel manga Shura no Toki. This details the thousand-year history of Mutsu Enmei Ryuu and the Mutsu family. It has arcs for each of the major periods in Japanese history, each with different characters. This was published at a slower pace. In total, there were 15 volumes. The series ended in 2005.
The anime adaptation of Shura no Toki occurred in 2004. They chose to adapt Shura no Toki rather than Shura no Mon, and covered 3 story arcs. Given the timing, this made more sense. Shura no Mon hadn't been released for 8 years, but Shura no Toki was still publishing and nearing its end, which is a good time for an anime adaptation. Of course, given the nature of the work, they adapted it in arcs rather than just doing a single one.
It's a bit of a historical accident that Shura no Toki got an anime adaptation, while Shura no Mon didn't. I don't think there's a single really convincing reason why it happened. Partially, the timing wasn't great. Martial arts was big in the 1980s, but by the mid-90s (when an anime might have started) it had died down in popularity. Shura no Toki was better timed in that respect and also had the benefit of being more historically themed (and hence appealing to a larger group than just martial arts enthusiasts). There's plenty of other speculation as to why the prequel was the only part to be adapted as an anime, but in any event that's the fact of the matter.
So the reason why Shura no Toki took that approach is because it was always designed and intended as a prequel to Shura no Mon, which has the more traditional single protagonist. However, in English, the Shura no Toki anime is the only one with a sizable following since neither manga is well known. Without that context, the style of the anime seems somewhat strange.