Second Thought
A picture is worth a thousand words. Not always.

A picture or a graphical depiction attracts attention and elicits a subjective response. Words can pack a punch and they can guide us to understand, think and act. Both have their rightful places.
If words are being relegated to being questioned on their existence in persuasive communication, how about saving money and time on reading, writing and learning about the hues and vagaries of life that we do to become better thinkers and communicators?
A picture without a single word is open to interpretations based on the beholder's perception and capabilities. Even a single word along with the visual can drive home the desired points) of the communicator. Otherwise, it's like an art piece.
In advertising or in any form of communication where you intend to trigger behavioural change, there's no fixed edge of any one of these-only visuals, only copy (text), long copy, short copy, copy & visual etc.
Whatever combination contextually works, is good.
Every single element of a created communication tool must be well thought through- whether it's a picture, a word or a cluster of words, an icon, the hues & shades, the graphical statement or even a dot. A coherent and meaningful whole possesses the power to be an effective piece of communication.