While the proposal of all statements requiring citation is obviously overshooting, I believe we all agree that more/better citations improve Wikidata.
One component here would be a social one, namely that it first becomes good practice, then the default, to cite statements.
For that, improved technology and new approaches are required. Suggestions include:
* Open a blank reference box when adding a statement in the default editor, thus subtly prompting a reference
* Show a "smart field" for reference adding, e.g. just paste a URL, and it registers it's an URL, suggests a title from the page at the URL, adds access date, suggests other data that can be inferred from the URL or the linked page, shows likely other fields (e.g. "author" or such) for easy fill-in
* Automatically add references for statements via external IDs. I have a bot that does that to some degree, but it could use productizing