The, already pathetic, conviction rate will get even worse if this comes into play though.
It's already been proven that jurors are less likely to convict if the death penalty would be the result, so all that will happen is abusers and paedophiles won't be convicted at all.
I totally get the anger, and on an emotional level I think abusers and paedophile deserve to be shot.
On a practical level though it's unworkable.
Look at the abortion laws in America, for example, many women campaigned and campaigned to get the right to their bodies restricted, and felt they achieved something great by doing so, until it started to impact them, many women have come out now and said they were monumentally wrong because they didn't understand the full impact of giving up their rights, they thought it would only effect other people.
That's exactly what would happen here. The state gets the right to enforce sterilisation on some people, and people, like a lot on this thread, would celebrate and think it was amazing, until they, or someone they know was impacted by the law.