Colourfastness and archival stability would be the main two advantages. The best we had in the old days (and the best that can still be done with light-sensitive methods) was Cibachrome (or Ilfochrome, as it became). It has pretty good colour stability over time, but the synthetic ground does not have known archival properties, and the dyes, while the best that have ever been developed, are still quite fugitive in comparison to stable pigments -- and you're not getting Ilfochromes when you opt for optical/chemical printing.

Printing with stable pigmented inks on paper with a proven record (cotton or linen rag -- not that the brand sold as paper for inkjet/giclée printing would have much of a history) makes the work sound as an œuvre d'art rather than a bit of ephemera. With the right paper and inks, and framed and displayed properly, there's no reason why a pigment print shouldn't last as long as a watercolour. (And the pigments being used these days are much better behaved than any of the brighter colours that watercolourists were using in the nineteenth and early twentieth centuries.)

Of course, there's quite a cut being taken for providing the upgrade in permanence -- even though the papers are relatively expensive, the inks are far from free, and it takes a lot longer to print, that's not enough to justify the size of the price jump. There is a prestige tax attached as well. It's not about the quality of the print per se -- a photographic print can have greater depth and vibrance (as can an inkjet print on a synthetic ground) -- but longevity, and the importance that implies. If you are selling prints as fine art, then longevity is a reasonable customer expectation.