It might help to find and download some scripts that pause the timer and see how they use that switch. Because any script using that switch now is making use of the timer the way it's currently set up. That will give you some concrete examples of how it's being used now. Rather than trying to come up with various examples. It's usually difficult coming up with valid examples if you've never needed the functionality of something.

And as I mentioned before, I am almost positive I saw Khaled respond on this years ago saying that it was by design. Searching isn't the best on this forum, so finding that might not be possible and may have been over 5 years ago anyhow. And perhaps I'm even remembering that incorrectly after so long. In any case, I don't think the current -p should be changed, though the help file could be reworded. It would be better to add a new switch to handle some other method of pausing timers so that it doesn't affect all scripts out there that currently use -p.