I agree with you that we don't have to tell them but show the readers, this way it makes a greater impact on the reader and your writing becomes more effective.
Short paragraphs are awesome because they make the reader feel as if there’s less to try to information to tackle and creates a flow. This is why newspapers use short paragraphs, there’s a better chance that the reader will read the entire article.
Writing is visual , it catches the eye before it has a chance to catch the brain. Short paragraphs put air around what you write and make it look inviting, whereas a long chunk of type can discourage a reader from even starting to read.