It's been said before, but this is all textbook academia. Chancellor Davenport is going to make the AD hire. It's not going to happen before she's actively serving, and it'd honestly be pretty abnormal to saddle a new chancellor with a hire at the level of an AD that's not of their choosing, this close to their start date. UT has a contract with Parker Executive Search but is under no obligation to actually use them for a search, and evidently doesn't want to here - probably Chancellor Davenport's prerogative. They'll name one when they name one. Clearly a bunch of Vols fans are up in arms over things playing out that way, but it's a university that participates in athletics, not an athletic club with some higher ed attached.
To do something other than how it's actively playing out right now would be putting the cart before the horse, from the perspective of the university. It just seems like a mess because this is Volnation and all we really care about here is the cart.