One of the most common things in most RPGs, in my experience, is the lack of certainty as to how to use the non-physical stats. If your character comes across a lowered portcullis, nobody expects you to actually demonstrate that you can lift it - although for your 18 strength fighter its not a challenge. But when the party comes across a riddle or a puzzle, the players are generally left to figure it out, without being able to say "My mage has an 18 intelligence, this would be simple".
But, if the GM did allow that, it does remove some of the enjoyment of the game.
Hawk