I think that... the biggest issue is "how does the seating arrangement actually look in practice, not principle?"
Basically, the question we are asking is, "who is actually in charge?"
For instance, if the Iron Bank can sabotage the entirety of the empire, but only by shooting themselves in the foot, and they are invested in not allowing such a state of affairs to come to pass if they can help it, checks and balances will naturally form, or be deliberately agreed upon as the deal is struck and the details come up for discussion.
But if it is impossible for them to singular target the state apparatus, I.E, cut us dry while the rest of the economy continues to function and the constituent regions rebel and drift away because the State is no longer capable of funding its military, paying the upkeep on its infrastructure, nor operating key pieces of state owned industry upon which everyone is somewhat reliant upon because Viserys also deliberately has a monopoly on certain things.
The question isn't, "can I make everyone around me which incidentally includes you" bleed, it is "can I make you bleed deliberately and get away with it more or less intact," which Viserys would never allow. It would be like us agreeing to become Braavos' attack dog in exchange for the scraps off their table, never acting out of turn for fear that they will neuter us financially while their careful network of alliances at least ensures they'll survive the tumult.
MAD is basically written into the contract to ensure both will never want to harm the other. But it is still implicit that the Bank would be subordinate to the state, not the other way around.
Now, that may not be the case in our reality, but Viserys is a dragon, so fat cat bankers' arguments are thus invalid.
