There should be a quick link from each Entity (Items as well as Properties) to the internal JSON representation of that Entity. A "download the raw data of this entity" link. I think this could be a perfect starting point for curious users that aren't afraid of digging into the guts of the repo.
Suggestion: The page
https://www.wikidata.org/w/index.php?title=Q7716283&action=info
should contain a link to
https://www.wikidata.org/wiki/Special:ApiSandbox#action=wbgetentities&ids=Q7716283
An other, much more visible solution could be a link at the bottom of each page.