I'm not going to get into discussing the rights and wrongs of shooting for 'sport'. Each to their own, but it's not my idea of fun.
I would agree to a point with the view that having each and every trap registered and identified is a bit bonkers. But consider that a properly set trap is more likely to be registered than an illegally set trap.
I shudder when I see some of the traps in our wild places, at least a registered trap is hopefully more humane in it's operation.