I concede with this and your earlier point, you don't need a blockchain to build a new banking system. The current banking system is evidence of that: there is no blockchain needed when you ask your bank sends your funds to another bank.
But if you want to build a system that is not wholly dependent on "banks" and centralized actors securing consensus of financial transactions - which is effectively Proof of Authority - you end up having to look at alternative consensus mechanisms like Proof of Work or Proof of Stake.
The same logic applies to something like game assets. People buy and sell game assets already without a blockchain, but they do so only through centralized custodians and intermediaries.
But if you want to build a system that is not wholly dependent on "banks" and centralized actors securing consensus of financial transactions - which is effectively Proof of Authority - you end up having to look at alternative consensus mechanisms like Proof of Work or Proof of Stake.
The same logic applies to something like game assets. People buy and sell game assets already without a blockchain, but they do so only through centralized custodians and intermediaries.