Don't forget that it's a lot easier to damage a screen protector than it is to damage the screen. So just because something scratched the protector, doesn't mean it would have definitely scratched the actual screen,
But yeah, if you've got the phone in an environment where it's likely to need it, for the sake of a few pounds you might as well.
I currently work on a site built on sand. My car seems to get a good sand blasting and I always land up with it in my pocket! So perhaps a good idea?