While I'm partial to your cynic interpretation — after all Cloudlfare is a for-profit US business —, the model isn't that far from what Jaron Lanier had proposed in ’Who Owns The Future?‘ (2010).

In the book he explains how these micropayments would be sent out to all the websites you visit, etc. And you can have a built-in mechanism to combat the "star system" that tech automatically enables, where a few people get the most money.

Lanier's proposal was that ISPs take charge of this issue, but perhaps Cloudflare can make it work. The less cynical interpretation would be that later they federate the system or even turn into a non-profit.

I don't think every website you visit should be paid. Who says this random website even deserves payment? This would incentivize people to use tricks to redirect traffic to their websites (which already happens..). Imagine a world where, in order to step into a retail store and browse the merchandise, you had to pay $0.25. Payment systems are already a nightmare, this would add headaches. And just because it's a non-profit or federated doesn't mean anything; show me a non-profit and I'll show you a hierarchical organization with a rich board, poor workers, and problematic outcomes.

People need to think long and hard about why they think there should be unlimited stuff on the internet. Have you looked around? It's mostly crap. Random scribblings by opinionated amateurs, exhibitionists shilling snake-oil, "products" like online games or unlimited videos designed to sell your personal information for a profit, "news" that is 100% gossip, and an unlimited number of echo chambers. We need less incentive for all this crap, not more. But ads are never going away, so it's moot.