I'm not sure the term "mining" has such negative connotations. Of course, it depends on one's own imagery. The first time I heard about it, it made me feel some Gold Rush vibes. I guess for someone already deeply involved in fighting against gold/coal/uranium/rare-earth elements mining, the term would indeed carry a negative connotation. My point is I don't believe the term to be widely perceived as bad. But that could change.

Also, the term "mining" is being used in other computer-related fields. See "Data Mining" for example. It doesn't seem to have a bad connotation there, meaning that the reason we could observe it in "Bitcoin Mining" is to seek elsewhere.