Electricity is ultimately a scare resource (burning coal, collecting sunlight), with the complication that it is being produced all the time so there are good reasons to try to offload usage to non-peak hours, as opposed to just reducing usage entirely.
Bandwidth is beguilingly similar to electricity, in that people access the internet via this huge network of wires, and there are similar peak usage problems.
Another similarity between electricity and bandwith is that non-usage can be wasteful--there has to be slack to accommodate burst and peak usage, but for the most part if communications infrastructure isn't being used to its full capacity it is being wasted; it's like building a six-lane highway that no one drives on. Similarly, particularly with fossil fuels, if power is generated but not used it just means that the fuel used to generate it was wasted. But there is a difference, in that electricity generation can be ramped up and down, while the amount of bandwidth available on given infrastructure remains fixed. (That's not to say that an individual user can't buy more bandwidth on demand, meaning that increased usage could cost an individual ISP more in, for example, transit costs; it's just that the total global bandwidth available remains fixed until someone installs more stuff, in the same sense that road capacity remains the same until more roads are built.) Also I suppose it doesn't matter too much if more solar or wind power is generated at a given moment than can be used--especially if it can be usefully stored in batteries or by pushing water uphill.
However I think drawing too many conclusions from the similarities between electricity and bandwith can lead to problems, because ultimately electricity is a scarce resource that is used up, while bandwith is mostly just a congestion problem. The idea situation is that all communications infrastructure would be used to just-below its peak capacity at all times. (Similarly it would be great, if impossible, if people's road trips were evenly distributed throughout the day--no rush hours or event congestion.) But there's no reason not to use as much bandwidth as is available--to the extent there can be waste the waste comes about from building unnecessary infrastructure. This seems very different than electricity where it always makes sense to try to reduce usage.
So, a per-bit metering system for bandwidth would likely be a bad policy because it would discourage usage all the time, but it makes no sense to discourage usage unless there is actual congestion. Thus while it might make sense to use pricing or other means to try to smooth out bandwidth usage or even to reduce it overall when infrastructure is nearing capacity, unlike with electricity encouraging "conservation" does not always make sense--instead you often want to encourage use of the infrastructure, and the best way to do this might be a metered price of zero.