I have only played the game once, but after that experience I do not see why anyone would bid on the Iron Throne track. The main advantage it offers is to go first, but I never could see a use in it. It always seems like it was best to go last, waiting to see opponents' actions. Holding the throne token also did not seem useful. Ties are not very common, especially ties involving you in particular, and unlike Dice Town, there is no material reward a player can offer you for picking them.
In my case, playing House Baratheon, it was even less useful, as being last makes Stannis more valuable.
The game is so well designed and deep that it feels like I am missing some large advantage that the track offers. What is its value?