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I have yet to see a "self-explanatory" example that wasn't either not self explanatory at all, not a trope or trope misuse. Nor has my imagination ever come up with such an entry.
Yes, the example format you are giving ("X is one") is bad.
"For a successful technology, reality must take precedence over public relations, for Nature cannot be fooled." - Richard FeynmanDo you mean the trope itself or the examples? For the examples, they can be cut with an edit reason, though the trend it to comment them out and leave a commented out note at the top of the page, stating "Zero Context Example entries are not allowed on wiki pages. All such entries have been commented out. Add context to the entries before uncommenting them."
What you describe is a Zero-Context Example. Those entry usually are commented out (by adding %% before them. That makes them invisible to readers, but editors can still notice them. It means enough context need to be added before they're allowed to be seen on the page.
Edit: ninja-ed by Terrie.
Edited by StFan

Could someone please confirm something for me, once and for all? I kind of want to cover my ass before I start quoting rules at someone. There is no such thing as a self-explanatory trope, correct? If it's on a trope list, it needs an explanation as to how it applies (and not just "X is one"), no exceptions.