Food for thought: http://www.straightdope.com/columns/read/2863/are-pit-bulls-really-all-that-dangerous
The middle ground is that all dogs pose an increased risk of a harmful biting attack. All owners should take reasonable steps to train their dog and keep them away from strangers and small unsupervised children.
No matter the precautions, other humans (usually children) will be bit. That's the inherent danger in life.
Knowing this, perhaps a training course for dog owners is necessary before a license to own is issued. I'm not sure how that will help, but it could be a middle ground.
Out right banning of breeds is radical and will not solve the problem, save for the obvious solution that less dogs = less attacks. '
I don't see evidence that the risk of owning a pit bull is so high that the only alternative is an outright ban of the breed.