The brand, in its current state, is relevant inside the boundaries of Tennessee's state lines, and that about as far as "tradition" is going to carry it. You see as many or more Florida/Alabama/Georgia and even Clemson stickers on Tennessee tagged cars outside of Knoxville proper these days.
You can talk " winning tradition" till you are blue in the face and trot out records from 70+ years ago all you want, and it still won't amount to anything in terms of whether or not we are relevant today. Winning is the only path to to even a modicum of relevancy in modern CFB.