But once you start doing aggregate stats instead of individual stats, you start to run into other problems. First, the math gets really weird. Let's say that I have a website that's getting 2% of all traffic. Now, let's say Netflix comes out and is insanely popular. My percentage drops to 1%, even though I have experienced zero drop in traffic. Because even though all of my users are still visiting the site exactly the same as they used to, people are spending more time online and they're spending more of it on Netflix.
The next problem you run into is distinguishing a site visit from a normal network request. So... what's a site visit? We can't go by bandwidth usage for obvious reasons, unless you want every site's homepage to weigh in at 300MB. So probably we go by request volume, and we ought to only allow requests for HTML resources, since otherwise people just stop bundling CSS and stick a thousand invisible images on every page.
Except now single-page apps don't work (maybe you think this is a positive) because they rely on regular AJAX requests. A micropayment system suffers from the same problem, but (assuming we're not foolish enough to build micropayments directly into browsers) it has the advantage of not being standardized, so you can have an individual site set up its own payment model. This cuts down on bad actors, because there's not a standardized set of rules to exploit, and because users have to consent to the system before they're charged -- ie, they're not giving someone money without knowledge just by clicking on a link.
Ignoring problems like that (and I think there are more that we could go into) what exactly is your goal? Is your goal to get people to make high-quality content? Because we already know that payment models based on clicks (micropayments included) bias towards low-quality, clickbait content. We've seen this on Youtube. We've seen it in news sites.
When just clicking on a link is enough to get someone money, and there's no advantage after clicking on that link to provide some kind of high-quality memorable content, then everyone who's investing in high-quality content is at a competitive disadvantage. Anyone who makes an app without twenty page refreshes is at a competitive disadvantage. Anyone who makes a news article that isn't paginated into 5 different screens is at a disadvantage.