Of course, you go to a centralized intermediary by removing the p2p action.
That's exactly what happens in crypto space, most use custodianship and intermediation rather than self-custody and p2p.
It is a matter of concept and philosophy.
Discussion
You’re comparing the fungibility of fiat banknotes (which relies on a central authority for their issuance) to Bitcoin. Actually with Bitcoin, it is the intermediaries that degrade the fungibility of Bitcoin.