Finney needs to go to the pod and get the ion readings going, but he also needs to get out of it before it is jettisoned. Makes perfect sense if the intent all along is to prepare the pod for jettisoning.
If you want to interpret that way then you need to be able to prove that launching the pod was part of the mission.
The episode made launching the pod contingent
on an emergency
condition when Red Alert is called.
In other words, when they flew into the ion storm they may or may not have an emergency
. The ion pod's mission would not have been included being ejected as a normal operation. But since having the pod was considered dangerous enough to jeopardize the ship, it was normal to have an extra button just to eject it in an emergency.
KIRK: Make it fast, Ben. I may have to go to Red Alert.
SHAW: Freeze that! If the court will notice, the log plainly shows the defendant's finger pressing the jettison button. The condition signal reads Yellow Alert. Not red alert, but simply Yellow Alert. When the pod containing Lieutenant Commander Finney was jettisoned, the emergency did not as yet exist.
If you want to argue about falling apart at the seams, why not address why Voyager's version of ST6 is different?
Oh, that's trivial - the entire point of the VOY episode was that it was a false dream. It was important that there be excessive, unreal death and suffering in the dream, as this was the established symptom of the disease Tuvok was suffering from.
The episode presented Tuvok's flashback as a legitimate part of Voyager history. It'd be trivial to just put TOS on a different continuity to account for the death on the Excelsior. It'll be like watching "Parallels" all over again