I strongly believe we should ban the breed, not the deed.
I also think bringing back dog licenses would be more workable than people think. All horses are now required to have passports and have been for some time- it's for different reasons, primarily linked to drugs and human consumption as well as identification. The thing is, although not everyone complies, the vast majority do, and it does help the problem. A properly enforced dog licensing system could work- or at least improve things.
When I was in sixth form, I worked in a dog boarding kennels, so came into contact with a wide range of dogs- the kennel was also involved in GSD and rottweiler re homing, yet I never met an aggressive member of either of these breeds. I never met a staffie that was dangerous, although a few of them were rather stupid :P
The two most aggressive dogs that stick in my mind were a chocolate lab and a lakeland terrier. The lab we knew was aggressive, so it was handled very carefully, and only by more experienced staff. It had been abused in the past, so its aggression was fear related. The lakeland terrier though was just awful- I have never met a dog like it- it would go for you, bite and not let go. Luckily it never bit me (although it did destroy a few pairs of my jeans. It did bite my colleague, leaving him with permanent scarring. I hope that dog was never allowed near a small child, as I do believe it was capable of killing one.
Banning breeds won't help- every dog can be taught to bite on command and be aggressive. Yes, some breeds can do more damage than others, but any big dog (e.g. labs, retrievers, setters, most hounds, pointers, great danes, newfoundlands etc) are more than capable of killing an adult without trouble and any dog can do serious harm to someone, especially a child or someone infirm.
The truth is, the DDA is totally unfit for purpose, and we need a proper law to focus on dog aggression, not the mess that currently exists.