I imagine that billing for the electricity usage will be the power company’s distant second concern behind the mechanical stress of hanging unauthorized devices off a cable that was not designed with this scenario in mind.
For example, See this video of how wires are inspected by humans crawling along them: https://youtu.be/oBJyyEAw-6g?si=QVqBgjqwlM4XCGKl
Big future for whoever can successfully commercialize this.
Of course they could create a sophisticated billing system, invest tens of millions in branding and marketing and then end up in the red for that particular operation.
Drone fleet operators would be paying more for ubiquitous access to drone parking on (presumably inspected and pre-approved segments of) powerlines. The energy supply is almost an ancillary service, but an important one.
Just like with EV charging today, the energy cost will presumably be higher than your household bill, or similar billing schemes. "The house always wins."
For example if a chain has a certified Weight Limit Load of 1 T, it means it actually lifted 4 T (or 10 T if it's certified to lift people). This is because a lifting sling is tested in very controllable environment when it's new, whereas on a building site it will be subject to dynamical stress caused by winds, it will be hit, it will be used in various temperatures etc.
Now, I'm not saying you're wrong: in case of power cables there might not be such a rigidly defined safety margin in law, and experts may figure out some assumptions, like the drones not operating during wind storms, in which the safety margin is more than needed - and therefore there's some spare capacity BEFORE the the actually needed safety margin.
As others said, I don't think the added weight of a drone would be a concern but i have no experience here.