Easily happen again... a third time? really? And I would not say at all that iconoclasts and iconodules were mostly just political! Granted, theology basically became what politics were for us...
"The whole city is full of it, the squares, the marketplaces, the crossroads, the alleyways; rag dealers, money-changers, food-sellers, they are busy arguing. If you ask someone to give you change, he philosophizes about the Begotten and the Unbegotten, if you inquire about the price of a loaf, you are told by way of reply that the Father is greater and the Son inferior; if you ask, "Is my bath ready?" the attendant answers that the Son was made out of nothing." - Gregory of Nyssa
Iconoclasm is one of the most boring heresies in the game though, because they do not have a patriarch and thus cannot follow that old route. I have to manually add a Iconoclast Patriarch!
Personally I feel you are ignoring the theological implications of icons, but I do not understand what you mean when you say " if there were currently both Orthodox and Catholic branches that have a greater difference from the mainstream path, but are still considered wholly within" do you mean churches within the church? So, like you might say that the church under the Moscow Patriarchate has more differences with the church under the Alexandrian Patriarchate, compared to the Orthodox Church and the Iconoclasts?