The one thing that made me wince was the statement that: "At present, charging an ordinary battery to deliver one unit of energy involves putting 2,000 units into it.". I don't think that's correct; it sounds way too inefficient.
A typical lithium-ion AA cell holds 750maH of charge... 2,000 times that would be 1,500 aH... or equivalent to charging at 100 amps for 15 hours? No way.
depends "what" you take into consideration. lets just say the 2,000x is a valid # for random benchmark sake... consider this (for fossil fuel, as an example) you need to hire 50 engineers to site the source, hire 500 engineers to design a platform, hire 5,000 dudes, to build the darn thing, (and all the energy that goes into these things, driving to work, running offices, then constructions materials, manufacturing cost of extracting the raw material and making the construction material, shipping the construction materials) ok. so you got the thing built... but haven't extracted anything and what kind of Ratio are we already at? then you get the goo out, you ship it (and you have to engineer the ships, build the ships, operate and fuel the ships) refine it - oh, you need to engineer a refinery, build a refinery, pay all those those people and consume all those resources...) so you got refined tuff.. now you need to distribute it... build trucks, consume fuel to get it there, build distribution stations, etc.. etc... etc... and at some point you have to decommission stuff, run operations to clean up stuff, etc.. so if you take the ENTIRE lifecycle cost and impact of producing and consuming energy (weather fossil or electric) then you start to get an idea that 2,000x might not be so far off.. most studies seem to agree electric (in all its varieties of source fuel) is ahead of fossil fuel in ratio of energy consumed to use. but its not a staggering difference. the biggest benefit is distribution to point of use for electricity is waaaay more efficient. (wire, instead of shipping and storing and distributing) - hence, why electricity is "cleaner" even if your apples to apples up through production. additionally you are "cleaner" at consumption. since a electric motor doesn't have quite the service of internal combustion engine, and the related cost/fuel there.
of course trying to "store" electricity in a box is not practical as fuel, to your point. but getting fuel into the box comes at a greater cost, if you don't need to box it, or can use what's in the box more efficiently - thats all the trick...
hence why buildings are wired to electricity and not piped with fossil fuel (since they don't have move around and carry their power on board, obviously)
the most efficient way to do that - is series electric hybrid - aka, the train. ...tune the IC to its most efficient (although very narrow) limits to consume on board energy storage (fossil fuel), and use the 3x more efficient a/c poly phase motor (electric) to drive.
anyway - my point is... the 2,000x # might be reasonable.