Azuregos can only be found horde side after a long quest chain, and after that through phasing, so alliance players can't really ever run into him.
As for a FoS, Onyxia got one because she was still going to exist, but at a different level. In other words, there would be two achievements for her. They added the FoS as a symbol that you had defeated her in the old mode as well as the new. Azuregos was simply removed, along with lots and lots else. There wasn't really a point in a FoS.
Seems like it would be a lot harder from a technological point of view. With an instance I would imagine that it would be a lot easier to track whether or not you finished it.