And it is funny (and perhaps even ironic) you should bring up that nursery rhyme. One of the very first things you learn when you study history is that in order to know the state of certain societies, read what they legislated, wanted to legislate, or warned against. No one legislates or warns against things that don't happen. The reason that is a nursery rhyme, rather than, say, "Sticks and stones may break my bones but bubbles never hurt me", is precisely because words do hurt.
But a much more profound thing to understand is that those who have power rarely need to exert it physically over others. Intimidation is enough, and is common in nature, too. Any sort of physical struggle bears a lot of risk for both sides involved (even if it's leopard vs. gazelle), so animals try to avoid violence by communicating their strength both to rivals in their own team as well as to potential prey or predators. It is called signalling (you can read about it here [1] and here [2]). Signalling is a very real thing in most (advanced) animals.
Obviously, being intimidated is not the same as being killed, but that doesn't mean it's not very real.