There are badges for asking questions, and there are badges for answering questions. But what about a badge for people that answer questions and do other things, but without ever asking questions. Maybe I'm so brilliant that I know all the answers (NO). Maybe I'm just afraid of asking my first question (Maybe). Maybe I just really enjoy helping folks get answers to their questions (Yes). But what about those users who give without taking? (If it could be characterized that way, which would be debatable, subjective, case-dependent) -- Do they (we) deserve a badge of their (our) own?
I'm not a fan of this idea. I realize that the reusable chunks of knowledge that stick around on these sites come from the answerers, so their contributions are very, very important. The fact that upvotes on answers count for more than upvotes on questions is clear evidence that SE (and likely much of the community) supports this position.
However, I would hate to see good, on-topic questions not get asked just because someone is trying to get this badge. The only way we get good answers, is for people to ask questions.
Overall, I don't feel like this badge would encourage good behavior; it would just discourage (some) good answerers from also asking decent questions.