I always assumed since the Farragut was in service and suffered the dikironium cloud creature attack in the 2250s that the crew complement was closer to 200, thus when 200 died that means Kirk would have been one of only a small handful of crew left alive, making his survival that much more poignant and the disaster all the more tragic.
Not quite. I had just watched "Obsession" and "Balance of Terror" after watching "A Quality of Mercy" so it maybe fresher for me to bring up. The Farragut had a crew of around 400 when she was attacked by the dikronium cloud creature.
Interestingly, around 3 years before the attack on Farragut (-11 Years to TOS S2), Pike's Enterprise curiously had a normal crew of 200-ish.
It's totally possible that the SNW Farragut might have received a smaller crew although they could've actually increased in crew as well to above 400...
From "Obsession"
SPOCK: Fortunately, I read somewhat faster. In brief, Doctor, nearly half the crew and the captain were annihilated. The captain's name was Garrovick.
MCCOY: The same as our Ensign.
SPOCK: His father. Among the survivors was a young officer on his first deep-space assignment, James T. Kirk. And there is still more. I suggest you study this.
...
MCCOY: Am I? I was speaking of Lieutenant James T. Kirk of the starship Farragut. Eleven years ago, you were the young officer at the phaser station when something attacked. According to the tapes, this young Lieutenant Kirk insisted upon blaming himself.
KIRK: Because I delayed in firing at it.
MCCOY: You had a normal emotion. You were startled. You delayed firing for a grand total of perhaps two seconds.
KIRK: If I hadn't delayed, it would have been killed.
MCCOY: The ship's exec didn't seem to think so. His log entry was quite clear on the subject. Lieutenant Kirk is a fine young officer who performed with uncommon bravery.
KIRK: Don't you understand? It killed two hundred crewmen.
MCCOY: Captain Garrovick was very important to you, wasn't he, Jim?
KIRK: Yes. He was my commanding officer from the day I left the Academy. One of the finest men I ever knew. I could have killed that thing if I'd fired soon enough the first time.
MCCOY: The same as our Ensign.
SPOCK: His father. Among the survivors was a young officer on his first deep-space assignment, James T. Kirk. And there is still more. I suggest you study this.
...
MCCOY: Am I? I was speaking of Lieutenant James T. Kirk of the starship Farragut. Eleven years ago, you were the young officer at the phaser station when something attacked. According to the tapes, this young Lieutenant Kirk insisted upon blaming himself.
KIRK: Because I delayed in firing at it.
MCCOY: You had a normal emotion. You were startled. You delayed firing for a grand total of perhaps two seconds.
KIRK: If I hadn't delayed, it would have been killed.
MCCOY: The ship's exec didn't seem to think so. His log entry was quite clear on the subject. Lieutenant Kirk is a fine young officer who performed with uncommon bravery.
KIRK: Don't you understand? It killed two hundred crewmen.
MCCOY: Captain Garrovick was very important to you, wasn't he, Jim?
KIRK: Yes. He was my commanding officer from the day I left the Academy. One of the finest men I ever knew. I could have killed that thing if I'd fired soon enough the first time.