For the article on Euler's conjecture, I am aware of this paper and that it serves as a sufficient proof of work for publication. It includes context for its purpose by citation, and the methods for verification were well-established. There is a class of literature where this type of structure works.

For the Kekule paper [1] there is a significant amount of information about the context and reasoning for the claim. This is not an isolated concept and he wrote at length as to why the idea might be plausible given the current evidence. He also could have written solely about the dream without context, but that lacks a grounding in the reality he was attempting to describe.

If it is possible to write a paper where the result is possible to verify using already-known methods, then by all means write in that style. But this is a subset of the useful papers to be written, and in my experience a small one.

[1] https://gallica.bnf.fr/ark:/12148/bpt6k281952v/f102.item