So with my knightly orders I tried as much as possible to make them different from each other as opposed to just “reskins” to use a video game term.
Having each order with a Valyrian blade feels a bit too samey – that they all were rich enough to buy one in the first place, that they had the same access to merchants from the great empire to the east, and so on.
Moreover, I think there’s something about the way that Valyrian blades work ini the setting, the way that they engender this obsession to have them, to take them, to never sell them, to pine after their loss, that would make it extremely difficult for a corporate body to own one. The temptation would be too strong for each man to try to claim the blade for their own House rather than let it pass later into the hands of a man from another House.