It is false that all paragraphs should have one main idea. A paragraph does not necessarily need a topic sentence when you write an essay. Because in an essay, there is already a topic given, all you have to do with the successive paragraphs you are writing is to write things related to the topic given. Every paragraph in the essay must be a subtopic to the overall topic therefore having another topic in each paragraph will make your essay incoherent and unparalleled in ideas perspective