It may be worth it. First export the report definition (File → Export → Export Report → Format: report definition). This should pop up a text file with pretty little information about the report, including all the data fields that are referenced. You can write a simple script to parse the file and spit out all of these fields.
I have never tried this before, so your mileage may vary. What you need to think about is what you mean by “displayed” fields. Fields cannot be directly displayed in the report, but can be used to calculate the formulas or summaries that are displayed. You need to think about this, as well as how your specific reports are written when you write your script.