If anything some of the larger blockchains “naturally” move towards a “central bank” like model.
Say you have a blockchain that requires you to sync 100’s of terabytes if not petabytes of information to setup a new node and 100’s of gigabytes a day to keep it upto date.
It’s not going to be feasible for individuals to talk to it directly.
Now you already have exchanges that keep ledgers other than the blockchain and that already do most of their transactions off the blockchain these are your banks.
In this model the blockchain essentially offers only value store for the exchanges and keeps only the exchanges honest this is essentially your central reserve.
The blockchain offers also a consensus protocol where either the miners if it’s PoW or the exchanges if it’s PoS hold the important seats, that’s your board of directors.
So yes I don’t think that current crypto is incapable of mimicking the model of banking we currently use some already do it unintentionally to some extent.
But currently there isn’t a single crypto that offers a built in fractional reserve and credit system as part of its blockchain its off possible to implement it.