He didn't have to be; as stated in dialogue, it was just Finney's turn on the duty roster.
What I mean is, no Lieutenant Commander should ever have been on that roster unless the task truly required a senior officer. Kirk isn't supposed to do his weekly shift at Phaser Control or Turbolift Maintenance, either.
The ion pod is mysterious in several ways:
1) What does it do? (Monitor ion storms for research purposes, supposedly. Kirk seemed to deliberately steer into that storm with the purpose of operating the pod in there.)
2) Why is it situated so that an ion storm threatens it? (Supposedly because exposure facilitates the measurements.)
3) Why is the response to that threat a jettisoning maneuver, rather than retraction or closing of shutters? (No idea there.)
4) Why is 1) a man-tended operation? (Might be related to the above. Perhaps the pod is extensively separated from the rest of the ship, and doesn't even enjoy computer connections.)
5) Why does the man need to be an officer, let alone a high-ranking one? (Again, might be related to above.)
Perhaps we could understand the role of the pod better if we understood ion storms better. Why does Kirk deliberately steer into one, and hang in there until his ship is on the verge of falling apart?
Timo Saloniemi