“A personal loan would be different from a loan from an institution of dubious legality, no? ” I don’t mean this as a ‘gotcha’ or anything, I’m asking because you’re the expert. Fundamentally, what’s the difference between house Lannister giving personal loans vs house Lannister establishing a bank and the bank giving personal loans?

The difference is whether we consider the bank a legal entity in its own right, one that can enter into contracts, sue and be sued, etc. Even today, with quite liberalized systems of general incorporation laws as opposed to requiring charters to incorporate, you still need to file paperwork to establish an LLC or an NGO or the like. 

So to give a modern analogy, let’s say I decide to open a bank – I rent some office space, hire some people to help me run the bank, put out a sign saying “Bank of Steve now open,” etc. If I don’t do the paperwork to establish the bank as a formal institution, I’m going to have some serious trouble if someone defaults on a mortgage, because the “Bank of Steve” can’t sue someone in court and the defaulter didn’t borrow any money from Steve Attewell personally. 

Moreover, banks do more than just give out loans. They also borrow money and invest money, they own real estate and other forms of property, they act as depository institutions, they act as financial middlemen, and so on and so forth. You need some legal framework to legalize these functions and to formalize how disputes that arise from these functions could be resolved.

So in the Westerosi context, without a royal charter that sets out the structure, rights, privileges, and limitations of the Bank, there’s no way to resolve major questions like: can the Bank own land? Who owns the lordship of that land, since “nulle terre sans seigneur”? Can the Bank be summoned to fight for the liege lord of that land, and can it be convicted of a felony if it doesn’t show up? (Likewise, can the Bank summon people to fight for it, and can it convict people of felonies for not showing up?) If someone who’s defaulted on their debt dies, does the Bank inherit their land or the eldest son of the defaulter?