Back in the late 80's, there was the CASE (Computer-Aided Software Engineering) fad, when it was thought diagrams could replace code.
The idea that a picture is worth a thousand words is not applicable to most of the words one would use to discuss systems designs. It is very difficult to discuss purpose and intent, or to present arguments that the design satisfies requirements or observes constraints, to justify choices, and say how things work, through any sort of diagram, let alone only those of UML (use cases are something of an exception, as they are not actually diagrams.)
On the other hand, diagrams are a very useful adjunct to these activities, and are widely used in informal discussions. This is broadly in line with how diagrams and pictures are used in other technical and scholarly fields: for example, maps, statistical charts and pictures of places and artifacts are very useful in history articles, but are never the full story.
Furthermore, I can usually write a thousand words faster than I can draw the corresponding UML diagram. The UML I am most likely to use will be machine-generated from code and will be used as a supplement to the text I am writing.