where im at the dogs that cause most problems are lurchers and greyhounds,ive known of quite a few small dogs being killed by them,just down the road we had a westie that was best mates with my staff got killed by a greyhound while walking on lead,i own a lurcher myself and dont want them banned or restricted.
imo its simple,just keep control of your dog on or off lead if not pay the price.
i wouldnt suggest that a lot of the well trained gun dogs with no inclination to chase anything for example should be on lead and muzzled by law,but fat pet labs are very common too and rarely trained