Oh dear. So you're taking the much stronger stance that it's not even just non-obvious to prove, it's non-obvious to intuit! If you are being honest, the set o

Oh dear. So you're taking the much stronger stance that it's not even just non-obvious to prove, it's non-obvious to intuit! If you are being honest, the set of numbers the fundamental theorem of arithmetic applies to is much more different from sets of objects it does not apply to than black swans are from white swans. Obviousness is probabilistic, so proving one seemingly obvious thing non-obvious doesn't mean we have to stop calling everything that seems obvious non-obvious, which is the implication of your analogy. Sets of objects that don't follow the fundamental theorem of arithmetic are already super non-obvious themselves, so it seems strange to use their features as an excuse to invalidate an obvious feature of the set of integers.