I find alternatives to "said" useful when writing non fiction (though obvs some of those words are not appropriate). When writing an academic essay and citing someone it can be difficult to incorporate the sources I want without using the same verbs over and over.
Words I use a lot:
writes, states, notes, offers, shows, explains, claims, asserts, argues, concedes, concludes.
Their varied meanings, of course, don't make them interchangeable, but by changing up the sentence structure and how I present the information (e.g. as a quote v. a summery) I can prevent myself from writing a paragraph full of "Smith argues... Smith argues... but Kim argues..."