What icons offer that's better than words, however, is rapid recognisability to those already familiar with that specific representation of the concept. This is why we have... road signs.
That's also why we don't allow just anyone to drive a car based on the fact they can operate it mechanically. We require they learn the iconography. We require they study them, commit them to memory, and we test them.
If they fail to understand the icons, they are not allowed to drive cars. And plenty of people fail this. Even when they're read books that explicitly state what each icon is depicting. When the icon's meaning has been made explicit to them, and isn't just relying on its efficacy of conceptual communication.
Icons are great additions to labels or great when used by a targeted audience.
They are lousy at all other times.
Hat tip to Chris Aldrich.