Big banks need to change their minds fast, otherwise they will crash, as people are already migrating to digital new banks much more friendly to crypto currency than the old ones.
If you sweep your funds into a cryptocurrency account, what cryptocurrency are you going to use to hold your funds?
I like that saying: never put all your eggs on the same basket. That is a good thought to remember when you want to invest your money. I see no reason to invest only in btc, although the biggest part of the crypto budget must be on it. It's better to check what are the up trend altcoins and share a percentage of your budget with them.
I am sure that right now banks are watching the many developments in the world of cryptocurrency and they are already thinking how they can join the digital revolution. Soon we are witnessing bank-sponsored cryptocurrency (which many can call as pseudo) which they can use in their own ecosystem.
As for cryptocurrency, it will always be bitcoin for me though I am also into Eth and XRP. There are actually good coins right now with bigger potential for growth. Sometimes it is just a matter of preference and some analysis.