It's less about transfer fees. I'm not saying you should make microtransactions to visit webpages.

I'm more imagining a mining-pool made up of webpage visitors. The website allocates you certain blocks of hashes to be calculated and you calculate those. Once they're calculated and the webpage verifies it by randomly double checking a few, then the webpage is served.

A websearch tell me a webpage visit nets the owners about ~2 cents in ad revenue. So you just need to mine some equivalent amount. It'd be sort of like a mining-pool where the overwhelming majority of users don't successfully mine a block - but when someone does the website owner gets the coin.

You could get more sophisticated on top of that and have some central mining-pool coordinator and session cookies etc so that your mining credit transfers across webpages and you can "premine" certain amounts

So the currency becomes more granular at "how many hashes have you calculated" and not how many coins do you have

I could be wrong though ~ It's possible 2 cents of hashes takes hours to crunch on a phone