Agreed with Tenacity that timidity in "Immunity Syndrome" would have served no purpose. Sure, probes were disappearing into the zone of darkness and not returning - but that would have been a valid way for Kirk's ship to operate, too. Just go in and kill the thing, since it needs killing and since there's nothing visible to fire at from the outside. Survival would be optional.
As for "The Galileo Seven", the very fact that the Murasaki phenomenon was there and wasn't going anywhere was telling enough - despite this, Starfleet had not been able to study it. Apparently, Kirk was taking a rare shortcut (supposedly because of the medicine delivery mission) and going where nobody would go again in years. Starships are busy things, after all. If Kirk has three days to use, why not use them? It's not as if the medicine mission would have been endangered in any way - Kirk made sure of that by only sending a shuttle.
What's odd about the episode is that Kirk stays there to search for the shuttle party. Why not leave them, since they aren't going anywhere, either? It's not as if they would have been in any sort of danger, equipped as they were with plenty of water and food and weapons. If they survived the supposed crash at all, they'd be fine. Just deliver the medicine and then return to continue the search. Heck, the other shuttle(s) could keep on searching while Kirk was delivering the medicine. Kirk could get tither and yon in the allocated three days, or at least in the episode he very much acts as if he can.
Note also that the mission was cleverly written as a rendezvous. The suffering masses would not suffer more if Kirk delayed, or less if Kirk hurried: they would only get their medicine after the three days were up and the second leg of the voyage of the vital vials began.
Kirk's ship not being a valid target in the virtual war? Why not? Surely the Vendikans would wish to shoot down any ship attempting to make friends with the Eminians, knowing that outsiders would swing the balance of the war. And while they'd actually do well to shoot at Kirk with live ammo there, they could also sort of rest assured that Anan 7 would do their dirty work for them - just like his granddad had done with the Valiant as far as the episode insinuates.
Timo Saloniemi