> With proper competition nobody would dare to introduce something like that, because people would just switch to one of the other ISPs in a heartbeat.

One of the ISPs would charge lower prices while offering crappier service. Some customers would still stick with it because it's cheaper. That ISP then strikes a deal with some smaller websites to make them faster than their competitors. Then the ISP offers a sweetheart deal to the larger competitors (at first) which they'll take to avoid losing ground, so then everybody is paying them for faster service.

Now that ISP has the lowest prices and their service is suddenly better because it's being subsidized by the websites, so they get more customers. Then they use the leverage of more customers to negotiate higher prices from the websites ad infinitum. The competitive advantage forces other websites to adopt the same business model.

It isn't a problem that competition solves because the people who have to pay can't choose between competing ISPs.