Q. “A word to the wise..” don’t the wise read whole books?

A. It means that “a word to the wise SUFFICES.” They pick up clues, they get the idea, they catch on quick, they tend to discern and understand without a need for everything to be explicity said – so they don’t need long speeches or detailed explanations. They get it.

Mishlei/Proverbs has a few verses that express this same point.