On the contrary, breed specific legislation HAS worked in a number of places.
Breed banning and breed specific legislation are NOT the same, so for those who oppose a total ban, there are many legislative options available to Vancouver that would make it more expensive and difficult to own these breeds.

Winnipeg banned Pit Bulls in 1990, and the number of attacks has dropped from 25 per year down to only 1-2 per year since the ban was enacted. Kitchener-Waterloo banned Pit Bulls in 1997, and their attack numbers have dropped from 18 during a two year period before the ban, to only 4 attacks over five years since the ban. Other areas in addition to Winnipeg and Kitchener-Waterloo that have either banned dangerous breeds (Pit Bulls, Rottweilers, Mastiffs), have enacted breed specific legislation, or have a combination of the two, are: Edmonton, most Nova Scotia municipalities, Saskatchewan (penalties here are the highest in Canada), MacDonald Manitoba, and eight Quebec municipalities.