I think we (us?) military historians tend to downplay the political element everpresent in the decisions of generals. Here, Bragg had lost Chattanooga and Knoxville, and he was under considerable pressure to retake both--as tokens visible to the public at large of the Confederacy's success in defending its territory. Knoxville and East TN were strategically important for their railroad connections and for supply, but also for political reasons. East TN had shown a tendency towards Unionism, which had (from the southern point of view) to be repressed. And the newly exiled Knoxville pro-Confederates would lobby for its retaking.
Put another way, even if Knoxville was, from a purely military point of view, not worth the taking (or retaking), leaders on both sides nevertheless believed its possession to be worth it.
This is not to endorse Bragg's decision to send Longstreet there. From a military point of view, success at the town he was already besieging was paramount. He didn't have the force to do both at once, plus success at Chattanooga would largely decide the fate of Knoxville.