> Because they both want to come home and use 3 kW for a half an hour at the same time, so the grid needs 6 kW of capacity just then.

Except that's not how it works on the large scale. If you have 1000 consumers coming home and using their 3 kW ovens for half an hour "at the same time", you very reliably get nowhere near 3 MW of load on the grid. For one, people do not in fact come home at the exact same time, and then, the exact switching intervals of the oven thermostats are essentially random, so the actual simultaneous load on the grid is pretty close to the thermal loss of all ovens combined, rather than the total peak power that they could consume if synchronized.

> No, you get compensated for not using what you paid for, not for not using what you normally use. If they're both not using then they both get paid. Obviously this gives the power company a good incentive not to have an overloaded grid.

So, the power company calculates the maximum energy that you could use given the service that you are buying, makes up some per-kWh price, multiplies the two, and then bills you that amount minus the kWh that you didn't use, and that gives the power company a good incentive not to have an overloaded grid?

Could you provide an example where the total of that bill wouldn't be identical to just billing the same per-kWh price multiplied with the kWh used?

> Now in practice what's going to happen is that the person who uses 3 kW for a half hour a day isn't going to buy 30 amp service for that, they're going to get 10 amp service and a 5 kWh battery that can run their oven or clothes drier from time to time and then slowly charge back up over 24 hours.

Well, that depends on the pricing? If it costs the same to buy 30 amp service and use 10 kWh per day as it costs to buy 10 amp service and use 10 kWh per day, why would I buy a 5 kWh battery?

> The analogy for broadband is you pay for 50Mbps service but it will burst up to 500Mbps for a few seconds at a time, so the person who doesn't use 24/7 has de facto 500Mbps instantaneous service for the price of 50Mbps.

So, the analogy to a hard rate limit where you have to operate your own energy storage is a setup where you can burst the service? I am not sure I get what you are trying to say.

> And it would make sense to sell broadband that way as well, with Mbps rather than amperes. Why can't I get 10Mbps during peak hours and gigabit the rest of the time? And then someone who needs 20Mbps during peak hours can get that and pay twice as much as me, even if I'm using a thousand times more data than them during off peak times.

Well, sure, that certainly could make some sense, but is completely orthogonal to whether billing happens based on Wh/bytes or W/bps? You also could have a time-dependent per-kWh or per-GB price, couldn't you? (And in the case of electricity, you usually can.)

> That's the entire marginal cost of moving a packet. The infrastructure cost is a fixed cost. You don't get it back if you don't send the packet and the network goes underutilized.

Well, infrastructure costs are fixed costs, yes, but infrastructure costs aren't fixed, as any given infrastructure has limited capacity. So, the marginal cost of one additional packet while you are under the capacity limit is a few femtocents (whatever the additional energy cost of moving that packet is, I haven't done the calculation), but the marginal cost of the next packet after you reach the capacity limit of some component is a few, possibly many, thousand bucks. Thus, the marginal cost that has to be used for calculating customer prices is the average over the range of realistic infrastructure expansion, which is quite a bit higher than the energy cost for an additional packet on existing infrastructure.

Also, wouldn't it follow from your argument that internet connectivity should be provided for free to most people? I mean, once you have the network built, it's a fixed cost, and providing service to an additional customer has nearly zero cost in most cases, so shouldn't people be able to sign up for free?