This is like the quest for the Holy Grail (which we all surely recall, was a cup, also). Something that can be used to heat water, melt snow, etc. and that can be carried easily on one's person.

The closest item commonly available is the bandaid container and even that is a pretty big pocket load. It does have seams, etc. but one will bear up for occasional use. It also makes for a good container for other elements of a minimalist kit.

If you want something sturdier, I feel the best solution is a cup that fits around the bottom of a canteen. I generally use a Nalgene canteen or a soda bottle equivalent, containing both canteen and cup in a cloth bag that I can either stash inside or onto a pack. Alternatively, I can carry the assembly on my belt.

There are lots of options for a canteen-conforming cup, ranging from a coffee can cheapest, but with seams) to stainless steel cups (not expensive, but heavy) to titanium (lightest, but expensive). There are similar cups for the GI canteen.

Being an old desert rat, I am not going to leave my canteen behind. I can think of only one situation where it was even possible - just one SAR ops where the pilot would only take a passenger with what they had on their person - no backpacks allowed, and that was an exceptional and unusual circumstance.

I think the real hangup is something that will fit comfortably in a pocket, but will be large enough to boil water for that nice cup of tea. Pretty difficult to find, unless you look at folding cups, and they present a lot of problems when used for heating.
Geezer in Chief