Butcher's done an outstanding job of keeping the literal angels that will vouchsafe Harry's character from the Council.
Have we seen Ancient Mai since Mouse testified on Harry's behalf, revealing that he's chosen to accept being Harry's pet? She might have converted on the spot politically- explains the Merlin's desperation.
From the Council's perspective, Harry is a loose cannon who deals freely with vampires, the nastier fae, and other monsters. He's worked with Nicodemus, the White Court, the Black Court; he has an unexplained knowledge of necromancy, Etruscan, and Sumerian yet struggles in Latin (this implies he practices the other two frequently, so dealings with White Court and ghouls); he starts the war with the Red Court, largely stays out of it (aside from eliminating the Tigress) until drafted, but then when they strike at his child he up and eliminates them all like they are nothing.
He's been known to throw Hellfire.
Yet he also has Soulfire and is close to the KotC. This should create cognitive distortion or cause the Senior Council to reconsider.
Has anyone seen him use Soulfire on the Council?
Have we seen Mai since Mouse testified on Harry's behalf?
Does anyone on the Council know that Harry is a frequent collaborator of the KotC- recall, they're not members of the Accords?
Do you think Battle Grounds will touch on this point, given the weapons Harry is wielding, and the implied revelation of his role as Warden?
EDIT: Going to add that from a Doylist POV, the point of Kemmler is throw suspicion on Harry, who appears to tick nearly all the same boxes. Which is part of why I am so confident that he was the last Starborn, and he used that ability specifically to seek knowledge beyond the Outer Gates.