Or the banks could just back their currency on Bitcoin... If not Bitcoin then their own proprietary blockchains. Just like several countries are in the process of doing right now.
Aside from that point, we don't need the internet to hold Bitcoin. It's not on a single website, either. You can't ever shut it down because it doesn't exist in one place. It's everywhere. I can store it on a piece of paper, too. I can even transfer it from my piece of paper to your piece of paper without the internet. Bitcoin isn't the 'end-all / be-all' solution to finance, by the way. There are dozens of viable platforms which outperform Bitcoin.
Omise_GO is a business similar to PayPal based in SE-Asia. They developed a blockchain for their platform which allows for faster and cheaper cash transfers.
There are dozens of companies like this; Litecoin, Ethereum, NEO, etc. Many are backed by their governments. I'm not sure why people still imagine that this is going away.
At this point it's too late and every big bank knows it. We're quickly entering the "If you can't beat'em, join'em" phase. The time to stop this technology was 9 years ago. It's way too late, now.
