One day banks will accept Bitcoin as medium of exchange and accept deposits from bitcoiners. As soon as the world powers accept it as medium of exchange.
Why would you want to send your Bitcoin to a bank when Bitcoin was literally created to work without banks and third parties? 
Even if they start accepting Bitcoin they would not allow you to withdraw whenever you want, they would charge additional fees, they would force you to use their ''approved'' wallet, and other crap like that.
So let's say i have .
20k in my paypal bank fed Insured gets 3.8% interest almost breaks even with inflation
And 1500 in my paypal account not insured.
Lastly 0.125 btc in my pay pal btc account. Grand total of 35000dollars .
Never spent any btc and stack it with buy the dip moves.
This means all the btc is 100% traceable kyc
And btc moons to 250k in two months I could simply sell that btc with zero issues of proof and pay tax easy easy.
And I also have 1 or 2 or 3 btc in a private wallet which is off the books more.
This is a reason for btc m held by a bank or bank style company [paypal]