Considering the tremendous congestion in the small Basra-Erbil corridor currently open over Iraq (UM860 and UM688) I doubt any western airline is taking specific detours to avoid Iranian airspace. The payment of fees for overflight and nav is probably an issue for US carriers, but others seem to have no issues. If you look at the traffic in the airspace there is an obvious dominance of the ME3 since they have to fly thru there to get to Europe, but a significant traffic from European carriers on tracks south of the Himalaya toward India and S.E. Asia.