The Iconians weren't on TOS just TNG and DS9.
Ok this is another foul for me. I don't know why but I was thinking The Guardian of Forever was an Iconian gate.
But even the fact they were featured a couple times as this ancient, powerful race could still give way to a story in the Alternate Reality only this time, we actually get to see them. It's a long shot but would also make a lot of people happy to have a movie in the series that deals with one of the primary themes of Star Trek.