Honestly, given that your bank most likely is processing your data using AI/LLMs anyway (after all, credit scores were one of the first applications of "big data" and "machine intelligence", back when that was mostly logistic regression over a handful of data points), why should I not also reap the benefits of that?
I think until proven otherwise, it's fair to consider financial data public information at this point. If we want to change that, I think it'll take way more than just not granting ChatGPT access to your bank account (although it'll definitely include it).
Cannot you feed your financial info to an LLM rather than give it full access to your account? The point of not giving it full access is also a matter of security of your account, more than about privacy.