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Premise 1: You can't add chaos to an inherently ordered system, while also maintaining the integrity of the system. In this case, the ordered system consists of a set of interdependent private Bank ledgers which, together with many other complex parts (physical security, credit agencies and scores, stock markets, counterfeits, etc), form the whole of the legacy banking system.
Premise 2: You can add order to an inherently chaotic system, thereby adding tangible functionality and value. You can do this repeatedly and cumulatively as the new system (in this case, a distributed digital ledger) asymptotically approaches perfection.
Premise 3: There is no possible way a pre-ordered, centrallized system can add the chaos (read: entropy) necessary to compete with the new system.