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I'd find it extremely useful if the File links list found on Image pages marked
which articles linked to it by "(inclusion)" through templates. Shouldn't be too
difficult, reasonably self-explanatory.

Not possible. Consider:
* Template:A: "[[Image:"
* Template:B: "Test.jpg]]"
* PageX: "{{A}}{{B}}"

Now the image is transcluded via {{A}} and {{B}} but not included in the templates themselves and there is no way for the software to know this.