Some trapping programs are considered necessary for public safety and wildlife management. Such programs are allowed everywhere in the world, even where recreational trapping is severely regulated. Ideally, they're conducted by professionals who are accountable for the results of their actions. Thus, ideally, they pose minimal risk to people and their companion animals.
Recreational trapping is continued as a sport, tradition, and industry. In some cases, it is also done in ways that aid public safely and wildlife management.
All of these forms of trapping can and should be done selectively, so that only the intended animals are caught, and so that incidental catches of non-target animals (including people's dogs) are minimized. (Of course, this ideal is rarely achieved, but let's remain theoretical for the moment).
Given all of the above, it's not a practical nor politically-viable option to "ban" or "outlaw" standard traps, nor trapping in general.