If the owners of the Banksy came out a few days later and claimed that someone else sold a fake Banksy NFT, but they're now going to sell the real NFT, the private keys won't help.
Only Banksy can mint an NFT for his artwork for it to be of ANY value. The same way that only Banksy can create Banksy art.
Public-private key encryption is how you verify that something was signed by the original author.
This can either be a crypto exchange (regulated on conversion to fiat, lest they get shut down by some SEC thing) or on those "vote on the blockchain" or "verified supply chain on the blockchain" things: eventually some non-blockchain entity has to be trusted enough to set state on the blockchain (e.g. "party A did indeed fulfill the contract to party B. please fulfill this smart contract", or "your food ingredient was prepared in accordance to your green/bio label's requirements").