This only really works if idle time is considered wasteful, but it's not. Electricity, battery life, cooling all come into effect. And to make a real squeeze out of those spare CPU cycles, JavaScript probably isn't the best choice.
There is also a bandwidth cost of delivering the application and sending the results.
But having said that, yes there is a cost, but there could also be a real gain for that cost. Replacing adverts with CPU cycles only changes the nature of paying indirectly for something. There should always be an easy way to opt out and users should know it's happening.
Imagine having 20 tabs opened solving stuff in background. Although modern browsers slow down the JS clock in the inactive tabs, it's still a killer for the CPU. The new equivalent of having adverts playing loud music and render video in 20 tabs (the music will be emitted by your CPU fan).
There is also a bandwidth cost of delivering the application and sending the results.
But having said that, yes there is a cost, but there could also be a real gain for that cost. Replacing adverts with CPU cycles only changes the nature of paying indirectly for something. There should always be an easy way to opt out and users should know it's happening.