Did you ever notice birds will sit on distribution wires? The distribution wire can be found along nearly every Main Street in town on wood poles usually with three to four wires. BUT you never see birds sitting on https://en.wikipedia.org/wiki/Electriciantransmission lines!
I suspect there may be 2 factors at play. At 6 digit voltages there is a corona around that wire and there also may be a lot of heat. HV lines are typically overloaded and run pretty hot. The eagles do sit on top of the poles for transmission wires.