Better skip the PoW part as it'll be wildly inefficient for most of the work done.

Instead, exchange web traffic for actual $. Say, some kind of tokens that are easily turned back into hard cash through a 3rd party.

Requesting a 100KB file? Okay, that'll be a $0.00002 token, please! (visitor's user agent provides it in a manner transparent to regular web users). Requesting a 3MB image? Okay, that'll be a $0.0005 token, please!

Result: niche websites earn hard cash. It doesn't matter much if you're hammered as long as the hammering comes with a corresponding flow of tokens (read: $). No token(s)? No service.

Regular web users would pay for those tokens through their normal internet service fees, and otherwise not be bothered. Massive scrapers would have to pay somehow for the tokens to be served web data at all.

In effect: put the bulk of public web sites behind a paywall. But with the bar low enough & in a manner that it's transparent for regular web users. Clicked "reload" by accident? Oops, internet service bill got upped by 2 micro-$.