It might be interesting, if, instead of balances, there were specific 'coins' in the protocol (at the moment, balances lose their individual identities, when they pass through a transaction)
Not true. Each transaction into an address is a separate coin, and they are redeemed separately when you spend them. They only mix when multiple coins are redeemed at the same time.
If you mean completely individual, non-mixing coins, I don't think there's a practical way to do it with a Bitcoin-like cryptocurrency. The blockchain would become huge.