The abilities of the various NPC Artisans evolved quite a bit during Diablo III’s development. When the Artisans were first introduced, their abilities were quite different than what we see in the game today. To bulletpoint the info from the original Artisan FAQ, released in August 2010:
It would take a whole news post just to explain all the changes there. Briefly; the Mystic is gone, skill rune items are gone, enchants are gone, there are no more ring or amulet crafting recipes, and as players are just realizing… there’s doesn’t seem to be any more item socketing either.
As you can see in that quote, the Blacksmith originally added sockets, while the Jeweler removed gems from sockets. Eventually the ability to socket was transferred to the Jeweler after he lost his jewelry crafting recipes, but shortly before release Risingred unearthed the final game version of the Jeweler’s interface, and noticed that his tab for socketing items was gone.
Players wondered if that was some temporary thing, or maybe it was an ability earned by leveling up the Jeweler. Turns out that’s not the case, as players have leveled that NPC all the way to max level 10, and his interface remains just the same. See the thumb of it below at level 10 for proof.
This seems to be an undocumented feature and a recent change, as the official site still lists Socketing Items as one of the Jeweler’s 3 abilities. Assuming this isn’t just a bug, which seems very unlikely, it looks like the developers wanted to make socketed items more rare and special by removing the ability for players to create them? Likely this is another of the advanced item features, such as the Talisman, Charms, crafting jewelery, the Mystic’s Enchants, and others that were all removed during development in order to simplify the item mechanics in D3C, while saving more complexity of features for D3X and D3Y.