As "The Naked Time" was supposed to depict the crew acting out of character, had it been the debut, you wouldn'y know them in character.
(Of course, TNG used their "remake" of this story very early, as I recall.)
Actually, "The Naked Time", *did* show them in character. The whole point was to show what was really inside them, without their masks on.
Exactly. "The Naked Time" showed the emotional demons that each character kept buried deep within especially with the two leads, Kirk and Spock.
For Spock, it was his submerged emotions and human side. For Kirk, it was his lonliness ("No Beach to Walk On"). Both of which came out during their confrontation in the briefing room.
However, if I were to choose the first episode to air, I'd have gone with the thrid filmed, "The Corbomite Maneuver" because it gives us a "day in the life" event aboard the starship Enterprise and introduces the characters, their roles and very much gives us the impression that he ship is alone in the night.