Most of the time when there is a threat or encounter with something foreign, Worf, as chief of security from season 2 of TNG onwards, recommends to load and arm torpedoes and phasers, normally followed by recommending firing them. Picard normally rejects this recommendation. Is there ever any time when Picard agrees that the best course of action is to fire torpedoes and phasers? (Note - I am not asking about a situation where the Enterprise/Federation is already at war, but more like a first-contact situation.)
Do the movies count? If so, I think First Contact would be a perfect example for this. Okay, it's against the Borg and Worf isn't technically still part of the crew, yet Picard's first reaction is to assuming command over the remainders of the fleet and immediately transmitting coordinates to fire at - not just for the Enterprise, but for all remaining ships. While Worf isn't on the Enterprise at that moment, he clearly agrees and doesn't want to abandon the Defiant to continue fighting. Overall, the whole movie depicts a quite aggressive Picard and he obviously doesn't stop trying to "murder" the Borg later on during the Holodeck scenes.
I've noticed this too. I've been watching TNG from day one and have taped every episode. Not once to my memory has Worf's recommendation to fire first EVER been taken. There has to be a T.V. Trope in there somewhere. It almost seems that Worf is being used as a foil to illustrate that 'aggression' is almost never warranted and is just a savage reaction. So he's 'put in his place' and proved wrong time after time.