There are some potential conflicts between banks and crypto. For example, banks are concerned that crypto could reduce the use of fiat currency and reduce their revenue from services such as credit cards and loans. Additionally, banks are concerned that crypto could be used for illegal activities such as money laundering and terrorist financing.
The modern banking system relies on fractional reserve banking, and crypto would essentially disallow banks from doing so. Fractional reserve banking only works because the government usually acts as arbiter with an infinite balance in case the bank goes under which is why banks would be reluctant to adopt more crypto into their portfolio.
The government hasn't hesitated in the past to bail out private banks, so it remains within their interest to act recklessly with depositor funds and be bailed out with no penalty.