Gregory: I've longed for someone to mass produce such a pot. Yes, it would be only for boiling water as it would be bothersome to clean (although maybe a custom cut-out scrubbie on a stick could get in there and clean it. I'll also note that the very hot water and alkaline detergents in a home dishwasher are quite good at cleaning pots without scrubbing). But it could be more efficient than the "flux ring" HX on the bottom of pots.
What you call "slices" are usually called "fins" in heat exchange design. And, yes, those mounted inside the inner tube would also help increase efficiency.
From heat exchange design literature and what I've measured in different configurations, rough numbers:
simple pot on a stove: 30% efficient
pot with HX on the bottom: 50% efficient
pot with finned inner chimney (like your gas water heater): 70-80% efficient.
So there is the potential to more than half your fuel consumption and boil times compared to a non-HX pot. Also, the outside of the pot is always below boiling so many materials could be used as an insulating cozy to reduce avoid heat losses.
Multiple such tubes would be classic boiler design, but for reasons of weight, manufacturing costs and cleanup, a single inner tube with pretty dense fins at the bottom would be preferred.
I've prowled around cooking and thrift stoves to see if something was close enough to modify. Bundt pans have the inner tube but are far too wide, short and heavy. Stainless-steel insulated "thermos" mugs are water tight and the normal place to put liquid could be the "chimney" with water in the annular space around it. But that annular space is a very small volume.
Additional, obvious fuel-saving idea: You need a lid for a pot. If your lid is the bottom of another pot, with, say snow in it, efficiencies for your tube-in-tube pot could go over 80%. Then the melted snow / pre-heated water becomes the feed for your next pot of tea. No, it's not UL, but for extended winter camping and base-camp use, an extra 100-200 grams of pot could save many kg of fuel.
