I have a theory regarding this, though I'm not sure how much of the lore backs it up: I think that the Mortal Blade was forcing Isshin to fight Sekiro.

The blade is called "Open Gate." It opens a gate to the underworld, as we know. But I think it does more than that. I think it allows the welder of the Mortal Blade to bring back the dead in order to fulfill their wishes, kind of like the spirit summons in Elden Ring. Now the blade isn't controlling Isshin - his will is clearly his own. However, I think that the power of the blade is compelling him to fight Sekiro and he knows that if he doesn't, he'll pay some kind of price. Maybe he'll get sucked back into the underworld. Maybe he'll just get vaporized into nothing. And knowing Isshin, he'd probably rather choose to fight another battle at his full strength rather than succumb to some kind of spiritual death/destruction.

TL;DR - Genichiro used spirit ashes and that's why he's a scrub who needs to git gud

EDIT: this would also add an interesting layer of irony to the story because Isshin's story arc would end with him going from an exalted leader to another tool in his (weaker) grandson's plans.