There is no possible way for a bank to 'prove' that the billion-dollar balance of a Walmart account represents anything of value. They can show that their systems reflect it, but it ends there. They can not prove that, say, $500 million of that balance is invented 'funny money' that represents absolutely nothing. Cryptocurrencies can not have this happen, as they manage their reliance on trust. I can prove a bitcoin is legitimate mathematically, and I need ask nothing of the other party for them to be able to verify it themselves. I can not prove a dollar displayed as part of my account balance at a bank is legitimate. And, as far as I understand matters, neither can anyone else. I must ask the other party to trust my bank, or trust the FDIC, or trust the US governments computer systems, or something along those lines.
The ideal situation, of course, would be a government-backed cryptocurrency with the government guaranteeing that the cryptocurrency would be honored as legal tender. But the political clout of banks makes such a thing very difficult. It would place banks in a position of actually earning their profits through the lending and borrowing of money, rather than actually profiting from garnering nearly every single monetary transaction which occurs (solely those which are conducted purely in cash exempted) in the economy in an act of cryptotaxation (the crypto prefix here meaning 'hidden', not related to cryptography).