Because of their lack of knowledge, and unlike Wizards, Alchemists didn't completely understand the Lightning Element and ended up creating Sparks (their version of Shock) combining Wind and Fire through an alchemical process. This made the spell unstable and impossible to keep going on for longer than fifteen seconds. And so the Royal Alchemists signed a pact with the Fomors and hid the pages of the Spell deep inside the Shadow Realm.
After torturing Berched and Lassar, Royal Alchemists found a way to Crystallize Intermediate Magic. They experimented for many years in the Shadow Realm (this evidence further proves that the Royal Alchemists are in good terms with the Fomors); this is why Inter Magic Crystals can be found in the Shadow Real occasionally.
Scholars Cryosite and Chiyuri have some hard facts that support the existence of an ancient Wizard society:
I don't think it would be too hard to fit it in storyline either. Much how the Ailech Regime opened the ranks of the Royal Alchemists to Milletians, perhaps the church of Lymilarks could also.
Actually storywise.. there was a Magic society before that was under command of the royality. But it was replaced by the Royal Alchemist for their achivements in the shadow world.
Recent rumors of the Archmage Society reassembling have reached the Nation.