Tried it.

See https://www.google.com/contributor/welcome/.

Users who don't like ads can just run an ad-blocker, so this hypothetical service would be competing with free, and would only convert the fraction who feel guilty enough about running ad-block to pay what the publisher charges.

The bigger sites will already have set up such a system, so you're left chasing smaller sites. The smaller ones are probably already on AdSense, so Google's experiment with Contributor will address them.