For the last 500+ years Banking has been around. It's part of our western culture. It's kind of presumptuous to proclaim the end of Banking with the coming of Bitcoin.
I remember years back when i first discovered Bitcoin. I was a die-hard Bitcoin evangelist(i'm still one) who used to tell everybody that the end of Banking has come with Bitcoin. Here we are today with the little experience (It's a real hustle to keep ones bitcoin wallets secure and safe) that i've got with cryptocurrencies i prefer to admit that Banks are going to stay but banking as we knew it may change.

I'll like to have some part of my bitcoins or altcoins been "managed" by a bank that will keep the private keys and give me access to the public address only. I know that the Bank is insured in case of theft or hack of my wallets.

We can make the analogy with the era of Internet and TV or radio. At the dawn of Internet many proclaimed that TV and radio were over. Decades later they are still around but they've evolved to adapt in the current ecosystem.  

That said, the Medici's style of banking may end in the Bitcoin era but Banks will still be around.