They established early on that the captain doesn't go on away missions, so there weren't a ton of opportunities to give Picard action. Also whenever he was of the ship, he was surrounded by an android and a klingon so he didn't need to do any fighting.
They basically had to separate him from the rest of the crew any time they wanted him to fight anyone. Starship Mine was the only real opportunity they created for that.
Then yeah, in the movies they had a 70 year old man climbing up metal structures. That was a bit silly.
I think it's implied that Picard was more Kirk-like for a little while even after he was stabbed through the heart. The point of the episode was that if he weren't Kirk-like enough to get stabbed he would have never been noticed enough to become a command officer.