When you pay your water bill, you aren’t just paying for the upkeep of the pipes that brought the water to your house – you’re also paying for the production of that water. The internet should be no different.
Besides paying a fixed monthly cost to your ISP for the physical connection, there should be a tiny monetary amount – a fraction of a cent – attached to each HTTP request you make, that can go towards covering server costs. Currently sites have no choice but to pay for their upkeep with advertising. Replacing this with direct payments would drastically curtail the data broker and surveillance industry that currently lives off of it.
How server costs would be measured, and whether sites would be allowed to charge a premium on top of that (eliminating paywalls, but also making web browsing a much more price-weary activity) is up for debate.
But currently using the internet is like paying for a car, without paying road tax.
I rent a VPS for under 10 credits a month. Traffic is included. It gives me a centralised calendar & address book, media streaming, and also a website. I happily pay this money. There are no ads, or data mining. Hell, I wouldn’t even want money for each visitor. That would be presumptious.
I see that there is a problem for e.g. journalism though. Not relying on advertising would be nice. But not in the way you propose.