Remember that when the cable companies started they were competing with over-the-air TV. To convince people to switch to cable, they had to provide something valuable enough to justify the cost. Content was that thing.

The reason ISPs can charge both the customers and the content providers is because we have no other choice. Where I live I have a choice of two providers: Comcast or Verizon. My choices are: use one of these two, or have no Internet. Not much of a choice.

I've never thought of it that way. That's a very interesting way to look at it! Isn't netflix driving business up for ISPs? The faster ISP gets business? I could be mistaken though.

If you consider everything on the Internet to be content, then would that require ISPs to be paying every website that they load? They would, of course, pass that cost along to us with whatever markup they want. Enjoy your $24.99/month Netflix, delivered to you by Time Warner Cable! Want to use reddit too? That's another $3.99/month, but look at all those grumpy cats you get for that! Facebook is another $4.99/month, but you can't put a price on virtual friendship, right? :)

I think that the way the cable network works relative to the internet is a historical artifact versus modern parlance. My opinion is that precedent is not actually a guiding factor in how future arrangements should be determined.

The Internet is different in many ways, but notably because cable companies aren't doing peering and don't have to deal with the complex settlement of international data trafficking.