Power distribution lines are already a major inefficiency loss to the power company. It's unclear if there would be any additional parasitic loss from the recharging bot, the efficiency of the system as a whole could in fact be greater than if the bot plugged into a metered outlet.

Kind of suits the piracy debate rather well actually. :-)

If you put a coil up to a HVAC line and draw current from that coil, that is going to increase the impedance of the line and reduce the amount of power that can be delivered at the other end.

Yes, the energy loss would probably be tiny in proportion to the energy transmitted and the resistive loss on a power line, but it is nevertheless a real loss to the power company.

It could be more efficient than plugging the bot into a metered outlet, but the power company gets paid for energy drawn from a metered outlet.

By analogy, it is more efficient for a retail shop if you steal goods from their warehouse before they are stocked on the shelves than if you buy them off the shelves, but the first case is a net loss for the retail shop, while more efficient, because they don't derive any revenues, and the second case, while less efficient, leads to an increase in profit for the shop.

This is quite different from piracy, which has no direct marginal cost - copyright was created to allow the recovery of fixed costs on certain types of work when there are low marginal costs to production.

My understanding is that at transmission line voltages, a big source of power loss is via corona discharge.

There are electrons and ions moving near the power lines. Perhaps it's possible to obtain a some of that power at a low rate without coupling back-EMF to the lines.