I think the issue would be more that bitcoin is philosophically incompatible with services like that. Bitcoin is anonymous, so I could transfer my money to my

I think the issue would be more that bitcoin is philosophically incompatible with services like that. Bitcoin is anonymous, so I could transfer my money to my account at another bank, report fraud, and the bank could never know unless the other bank told them. If the other bank tells them, or you set up a centralized register of transfers or accounts, you're just mirroring the current systems. Bitcoin doesn't have The Man, so there's no motivation not to do so fraudulently - what's the worst that happens if a bank realizes you're trying to defraud them? You've already moved your money elsewhere.