In the traditional financial system, the regulator will monitor your operations in order to maintain the integrity of the system, and the process will incur large costs and may be full of fraud. But the blockchain system gains integrity by incentivizing the best interests of the system and allowing anyone to verify it.
And that will depend on how transparent, immutable, decentralized the Banks Blockchain would be. If you take away some of the most important features like transparency, immutablity, decentralization, you would be attracting stronger regulation from central authority/government. The best way to keep them far away is to have no reason to be regulated by them.