There ain't many things more annoying than screensavers that make my fans spin up.
But who would get the coin?
I'd imagine a particularly good screensaver would be profit-sharing, but everyone else would run a free one and get all the mining income. Solo-mining is not really an option any more, and it'd be easy to cheat (detect wins & claim for yourself), so it'd have to be pool-based to be useful.
A charity. Everyone would love that.
Let's say you earn a percentage for running the screensaver.