I could be crazy, but I've kinda gotten the impression that mandates come from a noble trying to claim and item of type X and not finding it.
You aren't crazy for thinking that, but it still isn't correct. When a noble makes a mandate, they usually will claim at least one of what's made (at least if it's a trade good like a toy, craft, or mug), winding up with thirty of their usual mandate request laying on their bedroom floor. They'll also claim whatever they damn well please, which is usually the same thing as their mandate and will
also tend to wind up on their floor. But there's plenty of things they do not, in fact, claim, and there's plenty of times there will be eleventy trillion of something laying around and they mandate more of it anyways.
An example that sticks in my mind is from my last fort, where the Duchess/Countess/Baroness Consort kept demanding 3 Rose Gold Items. That's probably why it sticks in mind, since it turned her room magenta, but I digress. I always just made goblets for her, and she wound up with what seemed like fifty laying around, but I still had a fuckton sitting beneath* my trade depot waiting for me to get sick of them and either export them or melt them.
*I put my trade goods stockpile one z-level down and directly underneath the trade depot so that all my stuff is at the top of the list and my dwarves have the shortest possible distance to walk:
(etc.)
DEPOT
STUFF
(etc.)
Note: this is a side view