Well, the Iron Bank doesn’t try to destroy every other bank – after all, there are a number of other organizations that are lending money in large amounts in other nations (and indeed, the Iron Bank probably does a lot of business with other banks). Rather, they act against banks that rival their power.
But even then, the Iron Bank isn’t omnipotent. Dealing with the Rogare was a lot easier than dealing with a Westerosi bank would be, especially one with the explicit backing of a Great House, due to distance and the internal politics of the Free Cities. A Lannister Bank, for example, would be difficult to deal with, as Tywin’s hegemony within the Westerlands would make it difficult for the bank to find rebels to finance.