Ashi didn't ruin the season but she is emblematic of the real problem: With Season 5, Genndy completely changed the formula of Samurai Jack, and the transition was not graceful.
Samurai Jack (Seasons 1-4) was a show about a wandering samurai having achronological adventures in a weird sci-fi futurescape. "Getting back to the past" was never more than an excuse for Jack to meet new people and enter new situations. Each episode was self-contained, a movie unto itself.
Samurai Jack Season 5 flipped the script in almost every way. S1-4 was self-contained storytelling, S5 was serialized. S1-4 were relatively bloodless, S5 piled on the violence. S1-4 was straightforward and action-driven, S5 injected characterization and SO MUCH ANGST.
It's almost like Genndy felt uncomfortable with what he viewed as limitations within the framework of Samurai Jack and tried to make Season 5 more "legitimate storytelling". But the greatness of Samurai Jack was always in its craft, not necessarily its storytelling. The reason Samurai Jack was so compelling was because Genndy was a master at pacing, cinematography, and fight choreography. Every episode was a master class in how to entice a viewer through a slow build, then rewarding their patience with a loud, satisfying crescendo.
Samurai Jack 1-4 was a show that told simple stories spectacularly well. Season 5 told a more ambitious story in a clunky, uneven manner and ultimately it will not be remembered as fondly as a result.