Why does SWIFT messages cost money?

The SWIFT network is essentially the same thing as the Internet. It allows you to send messages from a BIC to another BIC. The BICs are like IP-addresses.

But sending messages over the SWIFT network is extremely expensive, a million times as expensive as The Internet. Why?

I cannot see why banks and financial institutions insist on using SWIFT, when they might as well use the Internet, and use public-key cryptography to verify and proove the validity of exchange messages.

It's just plain stupid.