No, there has to be a secondary market somewhere because professional diamond theft is a thing. So they have to be able to fence the diamonds somewhere. And this isn't a small time thing, either; there have been a few diamond heists in the past couple of decades in the tens of millions of dollars/pounds/euros each, involving serious professional criminals.

It's because diamonds are mostly untraceable. If you steal it, nobody can tell if a diamond sold 2 years ago was at one point stolen or not.

But actual diamond jewellery is mostly priced like artwork. The worth of the actual separate components has very little to do with the price of the item.