Jewelry isn't expensive because it is scarce, its expensive because people control its value very tightly.
The scenario you described is happening right now, diamonds are able to be made on an industrial scale cheaply, easily and on huge scales. Yet that hasn't impacted the De Beers profit in the slightest.
Because diamonds, real diamonds aren't made in a lab in an instant, they are made in the Earth over an eternity. So if you want your love to last eternity, instead of an instant, get a real diamond.
In short answer: What kind of jewelry would be valuable in a world where anything can be produced? The kind with the best marketing that appeals to its handmade authenticness, not its soulless creation by a machine.