Blockchains don't really offer anything a bank would need.
They have perfectly good ways of storing and processing transactions already. With Btc addresses and transactions are publicly visible. I don't want my bank account and details visible to the world. Unless you had unique, one shot payment addresses, it would be simple to create a wiki mapping addresses onto organisations and eventually people. Then there is processing. Btc only works as it pays miners to verify transactions. There is no way a bank would give over its processing to a third party that wasn't 100% legit. Would it run all its miners/verification in house? How do you explain the 51% threat to a bank?
The openness of block chains isn't really relevant to huge organisations.
They have perfectly good ways of storing and processing transactions already. With Btc addresses and transactions are publicly visible. I don't want my bank account and details visible to the world. Unless you had unique, one shot payment addresses, it would be simple to create a wiki mapping addresses onto organisations and eventually people. Then there is processing. Btc only works as it pays miners to verify transactions. There is no way a bank would give over its processing to a third party that wasn't 100% legit. Would it run all its miners/verification in house? How do you explain the 51% threat to a bank?
The openness of block chains isn't really relevant to huge organisations.
A private blockchain is like a local area network, the access is controlled locally. It is not open like Bitcoin.
There would be no 51% threat to the chain and the network could be maintained using minimal CPU power.
{Making it cheaper, and more profit for them} 
