It takes more than 10 minutes to provide a good answer to anything but the most basic questions, and most of those basic questions are duplicates. So this would also contribute to more users answering questions that should be closed, rather than performing the appropriate moderation actions.
Additionally, answers are rate limited so the system will prevent someone from achieving this. By including accepted answers as part of the criteria, you assume that accepted answers are correct (which they necessarily aren't correct and can be very wrong). The accepted answer portion of the proposal wouldn't even be possible since it takes 15 minutes before the OP is even allowed to accept an answer.
But beyond fixing the timing, which you did in a later revision, to even be feasible, we want to encourage quality, not quantity. How would this do that? I can't see this would encourage anything but quick rapid fire answers and not focusing on anything approaching quality.
In the end, badges exist to do one of two things:
- Badges should encourage positive behavior. As I've mentioned above, this would do the exact opposite.
- Badges should teach users about the features of this site. Rapid fire answers is certainly not a feature of the site, so I can't see where it would be teaching anyone anything about how the site works.