Hmmn, I don't think the Gunboat is an elite-only craft. Veteran pilots maybe . . . To me it's just a craft with a different role. The TIEs are all short ranged, the Gunboat is long-ranged, it's as simple as that. So the Gunboat does all the duties that its long-range enables, like scouting, patrolling, strike missions, etcetera. Its also the only non-elite fighter craft to mount Ion Cannons (the elite being the T/D), previously in the games the capture-duty was relegated to Stormtrooper Transports. The A/G gave them a fighter that can do it. You might also see them doing something as mundane as providing escort for transports while those transport perform customs inspections or what not. At the same time, you also see Gunboats in the Battle of Hoth cutscene, as they fly in support of the ground attack on the Rebel base. Maybe the TIE series, despite being able to enter an atmosphere, is actually of limited manoeuvrability therein. So the A/G provides a good atmospheric craft as well with all its control surfaces.
That's my view anyway. It's not necessarily superior to the TIE series, it's simply a fighter with a different operational role. Yeah it's got shields, but it needs them with its low manoeuvrability. TIEs rely on their speed and agility for defense.