Tuneboy lets you do all the same stuff the PCIII does and more. You just gotta know how to change things - for both PCIII and Tuneboy. Neither product will help you if you don't know what to do with it.
As far as, Classic tunes go, only Triumph engineers can say why they made different tunes for the Classics. If the engines and exhaust on the Classics are exactly the same as other Rockets, which they should be, then there isn't any reason for different tunes except to give them a different behavior. For the Classics, Triumph felt they should be restricted further in top speed (120 MPH) and they changed the low throttle maps, most likely to smoothen the boulevard parade cruise - not sure really.
As far as why can't Triumph's tunes eliminate popping and backfiring for everyone is because you can't have one perfect tune for everybody in the world - too many environmental variables change how a bike runs. Triumph chose to generalize the tune and make it richer than optimum to play things safe. That's about it.