Not sure ethereum is good here vs. privacy-first alternatives, but also not sure if all that is needed is Mechanical Turk, or a Stallman-esque browse-by-email. Maybe a protocol where people can get paid to run an email re-mixer as an onion service?
Build a system where users get paid to click random buttons, invoking services on onion sites. The hard part would be preventing side channel attacks... same request length, truly randomizing delay between task submission and completion (or some sort of subscription to send a block of random data regularly but sometimes it's user-controlled), no permanent logs vs. getting paid, etc.
Riffing on a few useless ideas here on a low-traffic day since the ideas are not going anywhere without execution.