They had something close to this with Google Contributor:

https://en.wikipedia.org/wiki/Google_Contributor

You add a few dollars to your online account, nominate which participating sites you want it to work with, and you would get an ad-free / paywall-free experience on those sites. The sites would determine the price per page - some only charged 1c, while some smaller blogs charged 5c. Some large Australian newspapers signed up, and apparently Mashable and The Onion were part of it at launch.

Ultimately every website I followed pulled out of the program. It seems that advertising revenue earns more for newspapers than anyone is prepared to pay for news. I never even used up the $5 I put into my Google Contributor account.