There isn't a literal throne because the Arbiter literally doesn't have a human body, look at her and look at Pelagos, they literally don't have legs/human body. How would they sit
It's silly to use this argument.
The central platform atop Oribos could be seen as the seat from which the Arbiter ruled. Indeed, it was the seat from which Zovaal the original Arbiter ruled.
Two things are worth noting about Turalyon:
1) He only leads Stormwind, not all of humanity.
2) The Race descriptions on the WoW website was recently updated. Despite the developments in Shadowlands, Anduin is still listed as leader of the Humans of stormwind (in-game the Human race).