Let's apply this practically, to known TOS episodes...
Consider those outings where Scotty is left in command of the Enterprise while Kirk, Spock and McCoy are away: "A Taste of Armageddon", "Friday's Child", "The Apple", "Metamorphosis", "Bread and Circuses" "The Enterprise Incident" and "The Empath" come to mind. Doohan/Scotty left some very good impressions in those stories, so much so that I don't think they would be as good without him. It isn't just the notion of having an engineer with a mathematical mind to run the ship while the captain and XO are away. It's Doohan's portrayal of Scott that left an impression there. The "personality" of the character made a material difference to the stories.
Consider those outings where Scotty is left in command of the Enterprise while Kirk, Spock and McCoy are away: "A Taste of Armageddon", "Friday's Child", "The Apple", "Metamorphosis", "Bread and Circuses" "The Enterprise Incident" and "The Empath" come to mind. Doohan/Scotty left some very good impressions in those stories, so much so that I don't think they would be as good without him. It isn't just the notion of having an engineer with a mathematical mind to run the ship while the captain and XO are away. It's Doohan's portrayal of Scott that left an impression there. The "personality" of the character made a material difference to the stories.