The point is that there's not really such a thing as a dangerous breed. There's dangerous dog owners though, and that's different. When you ban a breed, most of these owners will switch to a different breed (which inevitably rises in the dog bite statistics). That's mostly what that study showed, despite the ban on dangerous breeds, there weren't any fewer bite incidents.

it seems clear that any reduction in rate of ownership of dangerous breeds should reduce the overall bite rate

In theory, sure. But this assumes that certain breeds are inherently more dangerous, which is largely unproven. Most larger studies seem to dispute this.

(Coincidentally, France's restriction applies to all dangerous breeds

France's bite rate isn't substantially lower than neighbouring countries that don't have these bans. In practice, it seems these bans do little to nothing to reduce bites, which is an indicator that the breed isn't the issue.