Or, for that matter, the free-flyable observation gondola in Miyazaki's Laputa
In order for the sensor to work to full effect the Enterprise had to have her shields down when she entered the storm. If the shields conform to the shape of hull of the ship, the pod protruding out the side would prevent the shield from being fully raised, so the pod would have to be jettisoned to raise the shields.
I'd like to disagree on this, on two grounds.
First, the episode never mentions an issue with the ship's shields. And second, if the ship really were that vulnerable going in, I'd think Kirk would never even attempt the ion pod study...
Rather, if the pod really were a launchable device (and I undersign all of your speculation there), the necessity of launching the pod would come from Kirk wanting to get the hell out of there, which he naturally couldn't do until the pod was successfully launched. That's IMHO the simplest explanation...
That the pod itself would present a technobabble risk to the ship is often speculated, but that sounds like a needless complication, and isn't directly supported by the episode. The dialogue at least is fully compatible with the idea that Finney would have to prepare the pod for launch from the inside, then get out, and Kirk would fire the pod as soon as he possibly could - preferably so that Finney would have finished setting up the "readings on ion plates", but sooner if necessary, based on his personal judgement on the severity of the storm. Shields would be up the whole time, assuming they are of any use against ion storms.