The first is that you're assuming a race to the bottom where the banks will simply try to outspend each other on CPU. You can get a lot of the benefits of a blockchain where e.g. the 10 banks could all agree to each have 1 x86 box contributing to their part of the blockchain.
Any violation of such an agreement could be easily solved in meatspace, i.e. 9/10 remaining banks would just agree to ignore the chain maintained by the violator. Since they'd all recognize that they're getting /other/ benefits out of the blockchain without succumbing to some game-theory-esque race to the bottom.
Even if there's no such agreement the claim that any sort of alternate blockchain will use up the same resources as Bitcoin itself does is trivially refuted by various altcoins which use up less total CPU, since they're smaller networks.
The second faulty assumption is thinking that the only thing standing in the way of rewriting blockchain history is prohibitively expensive CPU resources. In the context of a "private" bank blockchain the banks could simply manually ignore a branch of the chain recognized as being produced by some malicious actor.
That leaves a bunch of valuable uses of the blockchain for banks. It's been mentioned as a replacement for the largely manual cross-bank money settling protocols they use now, replacing those with a blockchain would likely be much more secure and transparent, and any issues that arose by voluntarily running a "limited" blockchain would likely be smaller and more easily mitigated than whatever security issues their ad-hoc protocols have now.