Ever see a bad actor? One who reads the lines in the weird, stilted intonation of an automated phone system without any emotion or thought? If you test only by the testing script, without ever re-writing it or improvising around it, you are the QA equivalent of a fourth-grader in the school’s talent show. There is absolutely no way not to think of new tests while working; you are doing your product a disservice if you ignore these thoughts.
First, believing a test script is perfect is to ignore the premise of your profession – nothing is perfect. Second, even if the script were perfect according to the information available at the time of writing, surely you must have learned or thought about something new since then. Third, let’s say you’re wrong and the test you thought of is irrelevant or silly – at least you learned; your next test script will be better.
So please – don’t ignore yourself while testing. Your creativity is one of the reasons you’ve not been automated away.