It sounds like Sterling was some cool work - too bad it didn't work out. If it's going to happen, I think it's going to require a non-iterative step-change to get it right.
A far cleaner design for the web would be essentially an underlying payment system that governs all web traffic. You would essentially be paying for bytes, at a fairly low level. The issue is, people want to be completely unaware of the payment process so that their browsing habits are not perturbed. And yet at the same time, they must be able to trust that they won't be hit with a gotcha charge from some rent-collector troll site. You can't have both without some level of oversight, or some seriously negative consequences for people who set their "tolls" too high.
One of the biggest advantages of pay-to-play is deterrence of astroturfing and spam. If it costs money to send an email, the losers are the parasites who send millions of unwanted emails at everybody else's expense. But for these types of second-order social effects to take root, you really need a wide rollout.
The modern-day web is exactly backwards - it charges bots nothing and real humans everything. When a website is starved for bandwidth because demand for the content is higher than the web's ability to supply that content, it just breaks. It becomes the host's problem. In any other arena, the prices go up, and demand backs off until supply returns. Having tons of people demand the content you're serving from your website should be a _good_ thing, but right now it means you need to scale or die and cut off your revenue stream completely.
If it were profitable to be able to serve web content to people, then the decentralized web would become an obvious and inevitable reality, especially over the final mile. Rather than having to sign up for Comcast, they would make their money invisibly, behind the scenes, through the magical internet currency that was used to pay for bytes. You'd never have to talk to some fuck about your xfinity account again. No website would ever have to think about how to pivot into profitability. No youtube streamer would have to shill for products in the middle of their videos - the fact that you're watching it would be making youtube money directly, which youtube would pass on to the creators at a far more transparent way. No more demonetization because some companies might not want to be associated with you. Everything would be better. Everything. Making the web free is actually part of what led to its zombification.