Not having to put in money directly is one of the advantages of the approach. Aside from just convenience, hiding the true cost in this way will make it a lot more palatable for most people - if the device loses a bit of battery faster or gets warmer, it's not a big deal, but being forced to think about it in terms of direct payment will elicit more reactions of opting to just not go to as many websites.
If you just want for user to make it "palatable" you can produce the solution that doesn't involve mining and be "palatable." We are already having our batteries too drained by ads, that's a primary reason why I install add-block on the mobile.
I just want something where I can put in a few dollars and it goes to sites I visit. (Previous services have resembled this but with notable issues.)