Banks use tools as a store of value by holding some assets in reserves, for various economic benefits. Although, adopting Bitcoin in such capacity, would have it's pros and cons. Obviously like controlling inflationary trends, and even help stabilize the volatility of Bitcoin to its users,
Those other assets or store of value are regulated but bitcoin is not yet. So banks may not be able to come in yet and especially for the volatility. To regulate liquidity in bitcoin is pivotal to volatility and to do that requires KYC. So we need not be in a haste but be ready for KYC if banks have to become a third party to customer.
and conversely such volatility could also alter the stability of a banks statement of financial position. All these could add up to a more stable global economy. Surely banks have started to think of such prospect
They can't do any of those in isolation from the government. However, it doesn't point to the fact that the economy will be stable. Fiat isn't that volatile but the economy goes into recession and comes out of it and sometimes goes deeper in recession.