Another purpose: An excuse to add images or animations to tutorials. 😎
Personally, I seldom use Export variables. I try to do everything in the script code, because I think it's more reliable and easier to document.
However, when I'm experimenting with features or prototyping a new project, I may use them temporarily.
Here's an instance where Export variables were useful. It's code that runs in the Godot editor and tests a Godot add-on. Using Export variables avoids the need for the user to modify the script when changing the variables dir_readable and dir_writable:
https://github.com/daveTheOldCoder/Godot3To4FileConversion#test
The scripts that use the Export variables are test/CreateTestFilesGodot3/main.gd and test/ValidateTestFilesGodot4/main.gd.