Why did the practice of accounting in banking come to be structured around the automatic pairing of a scalar quantity with a vector one? Why do those accounts, by their own rules, insist upon the simultaneous recording of matching magnitudes of assets and liabilities?
I think the answer is custody - that banks look after other people's money. They hold it in safe and sceure custody. They are not permitted, under law and under their licence to be a bank, to spend that money in any way they please. They are custodians of property belonging to others.
THat's surely why a vector quantity must be involved, in order to denote the carrying (as from the Latin root of 'vector') of that money into other hands. A scalar quantity must also be involved to denote the value of the money. All is surely well in this world when custody of an externally-derived kind of financial equity is required. Specie and other kinds of commodity have long met that requirement of externality of origin.
What happened when, for example, precious metal was discovered? It arose as an asset of its owner, found in Nature. Did its value derive from a liability of the place where it was found or mined to its new owner? Is gold's value due to a financial debt carried by a goldmine? Surely not. It seems that an asset has arisen without a matching liability, and that must be because society has chosen not to apply accounting rules to physical goods derived from Nature. They are considered Nature's gifts, and we have chosen to say that their value is inherent. Their value isn't sourced fron Nature's liability to us. Nor has there been the mining of an equal amount of anti-gold from the goldmine, to keep the net equity of all physical goods equal to zero.
Switch focus to modern non-commodity money. In the latter part of the 19th century, writers such as Walter Bagehot pointed out that the amount of money in the world likely significantly exceeded the value of the known quantity of specie. So the world's money has, de facto, been 'off gold' for a long time, using a non-commodity basis - even if that's wasn't widely acknowledged by the authorities.
In a non-commodity money system, there are no foundational deposits of externally-derived value. Therefore, there is no sense of custody of external assets involved in money creation by fiat. The money assets arise and are created inside the system. They are therefore scalars. There is no need for any vectorial sense, to point to anything external when money comes into being by fiat. A scalar sense is all that's needed.
To follow accounting rules about the net-zero sum of assets and liabilities, that means an anti-valued internally-generated scalar must be created when a positively-valued internally-generated scalar (non-commodity fiat money) is created. There's no need for a vector, to carry anything to outside the money system.
Worse, if a vector were to be used and understood then something potentially fraudulent - a mispresentation - has surely occured. A debt has been conceived where none exists. An obligation to pass money outside the banking system seems to have arisen, that lacks the justification of a prior passing of money into it. New custody of deposited external value hasn't happened. No custody, no liability generated. Whoops.