A key aspect of a blockchain is that trust is obtained by distribution. The inability for a player to corrupt the ledger is what makes the ledger valuable/useful. Although public opinion on bitcoin might not be good, its decentralized nature is key to the security that has led companies like Nasdaq, NYSE, Barclay's, and Goldman Sachs to invest in bitcoin companies and exchanges. A completely internal blockchain is not a blockchain, it's a plain old database. Bitcoin is a bad word, but blockchain is a magical word on Wall Street atm. GS might be able to buy up a lot of BTC, but that wouldn't give them control over the network. They can't compete in hashing power, and that's the way that you get control. Their best avenue might be to lobby against it, but that is only getting more difficult, especially on a global scale. So yes, the bank's challenge is to create a blockchain that they can all agree to implement, and to agree upon a degree of distribution so that internal motivations at one cannot pervert the ledger (in the short run, of course they will eventually and fuck us all). One hope for bitcoin is that they cannot ever agree, or that it takes so long for them to agree, that the advantages are lost when compared to the popularity and evolved state of bitcoin.
Banks like to corrupt the ledger, though. That's how they roll. They have no vested interest in public trust, and if their instrument of public trust is a vehicle associated with drug deals, terrorism and blackmail they gain nothing from it. I'd argue that the banks have more incentive to make a database and call it a blockchain than adopt a blockchain and use it as a database.
Well, I do assume they will eventually go down the path of collusion. That's what they do. That said, right now they could all share a SQL database and each have read/write access to it. But I have to assume that someone, whether a regulator or someone from their own legal team, would object to that kind of a setup. UPDATE: IBM wants to be the one.