Seeing the reputation of the Earl, I guess it is obvious that purifying him wouldn’t be well-received with great admiration by society.
It isn’t even certain whether trying to have it disappear by extermination without purifying it would get admiration by society.
“Motive … false motive …” (Wendelin)
“Also, this Earl-sama wraith seems to be extremely obstinate considering the church’s holy magicians failed to get rid of it before.” (Ogas)