The bug

As mentioned in the title, non-op players can run op commands from signs (using "run_command" "clickEvent", MC-59653), but not from written books (also using the "run_command" "clickEvent" mechanic). If that's not a bug, it's definitely inconsistent.

How to reproduce

1. Create a new world with cheats disabled
2. Open the world to LAN with cheats enabled
3. Give yourself a written book with a "run_command" clickEvent:

   /give @s written_book[written_book_content={title:"MC-201807",author:"Author",pages:['{"text":"Test","clickEvent":{"action":"run_command","value":"/give @s stone"}}']}] 1

4. Close and reopen the world
5. Open the book and click on the word "Test"
   → The command fails (you are not given a block of stone)
6. Open the world to LAN again with cheats enabled
7. Open the book and click on the word "Test"
   → The command runs successfully (you are given a block of stone)