Words have an impact.
In the case of bullying it has led to multiple deaths. In the case of terrorist advocacy, it has led to repeated violent/racist protests that has led to countless people getting hurt and in some cases dying. No one should have the right to advocate violence against all members of an ethnic group. Just look at what's happening in France.
What you are proposing abridges freedom of speech. If a person decides to jump off a bridge because someone called them fat, too bad. We should have learned as a society that restrictions on actions do not make us safer unless those particular necessarily lead directly to harm of others. Advocating violence against an ethnic group, while reprehensible, should be protected speech. Shouting "Fire" in a crowded theater necessarily leads directly to the harm of others, so restrictions are acceptable.
What invariably ends up happening is government takes too much control. Just look at what's happening in England (to Tottenham's Yid Army or the ridiculously racist hit job the FA did on Luis Suarez for using the perfectly acceptable by South American standards word negrito). If you give government power, they will abuse it. Every time. The question should be: is the abuse worth it? In this case, definitely not.