Right now, the laser fence uses the same amount of power whether it's idle, recharging or even disconnected from any other fence posts. It would be nice if the constant drain would be rather low and proportional to the length of the supplied fence(s), and there was an additional high power usage for regenerating lost HP / re-establishing the fence after destruction.

Well I have some good news for you then: laser fences already consume twice as much power when they are charging or repairing a broken fence segment. As far as the scaling based on fence length, a month ago I would have told you that implementing it was more headache than it was worth but with the upcoming upgrades for energy efficiency, it isn't that much extra work to add it. No promises but if we can figure out a version of the mechanic that adds more immersion than confusion, then I will include it with the next major update.
Feel free to join the discord if you want join in the discussion as we hash out the details: https://discord.gg/freXKz5

Version 1.1.4 includes a rework to power consumption so now power consumption is proportional to fence length. It also includes upgrades to reduce the passive power consumption of Laser Fences