@Azel - I think you're somewhat exaggerating how much using the Iron Throne would 'wreck' our legitimacy as the successor to the Freehold. We can take steps to handle that, and we also need to make an effort to accommodate our Westerosi subjects. We're going to call ourselves Emperor of Valaryia
and Westeros, right? So we have signs and legitimacy from both the Freehold and Aegon the Conqueror's kingdom.
Look. What signs and legitimacy do we actually have in Essos?
Did we accept their cultural norms? Nope. We tossed out slavery as our very first act, which has a proud tradition there.
Did we make nice with the magisters? Nope. We killed a whole damn lot of them.
Did we maintain the policy of blood superiority determined by Valyrian ancestry? Nope. We are an equal opportunity employer and a whole lot of those vacancies left by magisters are being filled by people from any number of backgrounds.
What we are is a conqueror and so far, the one thing that helps us keep people in line is that they see us as a
Valyrian warlord, purely by dint of our lineage.
But what will happen when we assume the Barbaroi Chair and try to rule them while sitting on it? They will begin to question that nice little myth of the Freehold Reborn. They will look at our chair, at our actions, our title and conclude that we are, in fact, just a random conqueror. To Essos, the Iron Throne is a symbol of the backwards barbaroi kingdoms to the west and nobody who will step before us when we sit on it will be unable to notice that. Especially as, yet again, we have zero legitimacy except our lineage in Essos.
It would be like the western president / chancellor / similar titles going on a Hadj. No matter how innocent the matter might be, it would alienate a ton of people due to it's symbolism.
At the same time, all this vaunted symbolism is gone from the pointy chair. It was meant as a symbol of a united Westeros under Targ rule, which is legitimized by dragonfire. But the rebellion put and end to it. It was not dragons, but plain old swords that took the Iron Throne. They didn't seat Viserys on it and installed a comically self-serving regent, but flat out unseated the Targ line.
Now it's just a chair. One that anyone with enough swords can capture. And let's not pretend that our way of re-acquiring it will do it's supposed legend any favors. It will be yet another conquest by the sword fought over this throne, making it not more or less special then any other throne. Or the hill in a king-of-the-hill game. The nimbus of invincibility is already broken, leaving behind a symbol of Westerosi independence under whoever has the biggest army.
So what do we exactly get out of keeping that thing beside "cool throne"? Because I sure as hell am not looking forward to having to patch up the mess this will leave behind, just so that we can get half a paragraph about the throne and then never having it play any role what so ever again, except as a rallying point for Westerosi to want their independence back and for Essosi to get rid of the barbaroi warlord that subjugated them.
We are making a new realm and need new symbols. Aegon the Conqueror understood this. He took the crowns of the Westerosi kings away from them, then forged himself a throne that symbolized his rule.
Why should we shoot ourselves in the foot just for pointless shiny?