...Although best plot sense would be made if the pod were located close to Engineering, so that Finney could slip from the pod to his hideout unnoticed.
The location next to the shuttlebay in TOS-R is perfect in this respect. Nobody ever loiters near the shuttlebay, be it action stations or leisure. The lower sensor dome location in turn would be quite unideal.
As for the exact nature of the ion pod, and the mysterious reasons behind it requiring not just a person operating the thing in situ, but a high-ranking officer
... Debate rages. In modern thinking, automation should be capable of handling all measuring tasks that a human can handle, and of doing them better, too. But one might argue that the ion pod was a device intended to measure the effects of an ion storm on humans
. And Starfleet doesn't send low-ranking sailors to act as guinea pigs in dangerous experiments: it expects its officers to lead by example.
Another mystery is why the pod had to be jettisoned. Was it always intended to be jettisoned once Finney had prepared it? That would make perfect sense: a probe to be launched into the storm, with delicate experiments aboard that only a computer expert like Finney can prepare. And notice how Kirk deliberately steers into the storm. His ship could easily avoid it, but Kirk calmly commands the vessel to plunge ahead, perhaps with the purpose of launching the ion pod at a suitable point within the storm. But going too deep into the storm would endanger the ship, so there's a time limit on when the pod must be launched. Not too early, and not too late; and the exact moment cannot be divined until one is inside the storm and can tell exactly how severe it is and where the optimal "launch depth" lies. Hence, the launch is directly rigged to the Captain's command chair console...