The AAC is a little like UConn itself. Even if the teams are good, is there interest?
Rivalries enhance sports. For UConn, the AAC is not rich in rivalries because (1) there is little shared history and (2) there is not shared geography.
You might not reach Pow6r 6 in Football, but why sentence your basketball to Pow7r 7 status?
With the Big East you could be in a Top 3 basketball conference with more natural rivals. Keep FBS football - there is not much downside from your current football alignment.