It doesn't have to completely cover the costs, only offset it some and be used in conjunction with other income generation methods.

Personally, I don't mind it so long as it is both fully disclosed and the ramifications fully explained - both in an accessible manner to a layperson. So long as they do that, I'm okay with it. I'm more okay with it if they give the user a simple means to opt out in a meaningful fashion.

Now, chances are exactly none of those conditions will be met in the real world. But, in principle, I am okay with it.

Unless you just package it and let youtube do the actual streaming. Imagine creating "cat-videos.com" and embedding all the youtube videos into the site but providing a better UI for browsing them.

But you'd get both ads and mining. The point of mining was to get rid of ads!