How to restore old, scratched plates
Brasso (yes, the metal polish) works better than toothpaste in this case. It is a bit more grainy so works faster but doesn't damage the parts. It does take some work though that may or may not make sense depending on the rarity of the elements. 

And yes, with either toothpaste or Brasso, you actually have to vigorously rub the surface to buff it up. It might be easier and cheaper just to replace the worn parts with new ones if they really bother you.

LEGO getting scratched up a bit is normal. In most colors you won't even notice it, but there are certain colors where scratches are more visible&nbsp;— with black being the worst. So it actually helps to store black parts stuck together to prevent rubbing against each other in storage.