That would not preclude the owners being thrown in jail mind you. I have seen the massive facial scars on an 8 year old girl mauled by the families pit bull (that wouldn't ever hurt a fly). No different than leaving a loaded gun where a 3 year old could get to it. Call your city council person and suggest a new city ordinance.
How about responsible dog ownership laws? In places that have implemented such laws (and enforced them), there have been surprising results. For example, in Calgary, their serious attacks have dramatically declined, and their dog licensing is over 90%. They didn’t need to ban a breed or raise insurance amounts, and it still worked really well.
Prevention (forcing people to take responsibility) is the only thing so far that has had any impact on dog attacks.