Whether they would really be engaging it early or late, it wont really be still that changing a thing because even if they would be integrating Bitcoin investment or storage, then i dont really believe that
Direct involvement is possible, but we can guess what banks will do with cryptocurrencies.
They never like anyone to compete with them with instruments that are transparent and do not have full control.
Remember that banks are under the government and the government should have all the control.
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centralized or heavily regulated these institutions are which would really be entirely removing the essence of Bitcoins characteristics or purpose in the first place.
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So there is nothing to expect in integration with banks, as it will only lead us to the rule of existing institutions.
That would remove the essence of Bitcoin's decentralized characteristics.