The advantages of GMO food are usually to the producer or the farmer rather than the final consumer of the food.
That said, there's a few exceptions -- the Arctic Apple that doesn't brown so easily, the reduced carcinogen (all potatoes have acrylamide which is suspected to cause cancer) "Innate" potatoes, Golden Rice that provides vitamin A, etc. Since there's a difference (an advantage) to the end user, these things are indeed labelled voluntarily, because they're believed to be better.
But as for the seed that's sold to the farmer, absolutely, it's labelled. The farmer knows exactly what he's buying, and he knows why he's paying extra for it -- because for his purposes, it's better. (If it wasn't, he wouldn't buy it.)
But the end product, what he sells? It has no practical difference from the non-GMO variety, so there's no reason to label it as different except as a "scarlet letter" to be pushed for by the people who want to make their non-GMO foods look better than the the GMO varieties. Of course, they already have a label for that -- "organic" -- though to be fair, "organic" means more than simply non-GMO. (Though there are some non-GMO labels they can voluntarily use as well if they want.)
In any event, the organic certification allows crops altered with mutagenisis -- where things are treated with radiation or mutation inducing chemicals and they see what happens, and if they like it they keep it -- which always struck me as far more scary than anything involving transgenics which is much more controlled, but hey, our ruby red grapefruit, that's organic, even though it was made with mutagensis and not tested anywhere near as much as something made with transgenics, because of ... reasons.