No it makes no sense. Zotero and Mendeley and Papers don’t care about my document, just as Bibdesk doesn’t. They don’ even know it exists and happily fulfil all their functional requirements without it. That’s because Zotero and Mendeley and Papers themselves don’t have anything to do with inserting bibliography into documents. They may ship with additional components that enable this to occur, but this isn’t a core function of the tool itself, and one that is not used by all their users.
That is my material point.