What Bellrider says. And I believe the primary reason for bonding the helicopter and, more importantly, the crew's conductive suits onto the line is to eliminate the effects of the extremely high voltage gradient in the electric field strength that exists in very close proximity to the line. This gradient reaches thousands of volts/meter. It's not very survivable to have a thousand volt potential between your head and your feet. Birds get away with it because they are so small. The suit makes the voltage the same all over the body, thereby eliminating that problem. I have read that having a small "leak" or tear in a conductive suit leads to some rather unpleasant sensations
And to Bellrider's original point, the guys who work on these things while they are energized have to VERY carefully respect stand-off distances to tower components. Closing the gap between a tower component and the line below that afforded by the insulators lead to Very Bad Things.