The only problem I see with that is that to harvest power leakage of high voltage lines via induction would require a relatively long cable to obtain even a very small amount of power. I suppose the drones could carry spooled wires to lower, but it would take a long time to charge the capacity of batteries sufficient for this type of powered flight which, although very convenient and maneuverable for small craft, it extremely power hungry compared to other methods of flight. Basically, a drone would spend a good amount of time just leeching enough power to reel in the spool, let along spinning its rotors for flight.
A better design might be a drone with insulated claws to grab onto an electrified fence without shorting out and then physically touching the fence with an exposed conductor. Here you almost have the opposite problem. An electrified fence is running a lot higher current than mains power so, although you wouldn’t need as heavy a transformer as used on high power lines, it would have to be heavier than the wall wart or converter brick you might want to put into your drone.
The best option would be a purpose built roost delivering the correct DC voltage, perhaps built on top of electric vehicle charging stations.
