As a general rule of thumb, when a change in made in an AD or a prominent head coaching position - especially if the previous person left under a cloud - there is a tendency to hire someone who presents a contrast to the previous (failed) person.
Teague, from many accounts, alienated a lot of people at the U, in part because he was seen as not caring about the non-revenue sports. Therefore, I strongly suspect that the next AD will get the message that he or she has to play nice with the non-revenue sports and coaches. That does NOT mean they ignore the needs of the major revenue sports - but the next AD, at the very least, will be charged with maintaining good relationships with all of the sports.
one more thought - some AD's tend to be the administrative types - others tend to be the glad-handing, schmoozer types. if the U wants an administrative type, Goetz is already here and knows the landscape. If they want a schmoozer, I'm not sure that fits her profile.