A bank can own BTC. A bank can sell BTC. There is no obligation to adhere to the same regulations that apply to fiat aside from what is already established for you and I just because it is a bank. A bank can buy and sell cars, snow cones, or goats if they want (and often do in the case of recovered collateral). There is no way to stop banks from entering BTC. If we can say BTC cannot be owned by entity X, then the same can be said for person Y.
i guess you missed all of the central banking notifications of the world (china, canada, russia, bolivia, etc etc)
all announcing that central banks wont offer bitcoins directly.
banks have contracts with governments, mints, royalty, feds to only handle legal tender. as for recovering collateral. banks sell debt to private companies and these private companies grab physical goods and turn them into legal tender to then give back to banks.. (debt recovery agencies auctioning off property)
the real solution is not banks and regulation.. but insurance companies and lawyers whom would form the consumer protection people need