. . .
In the same context, going and tracking down the creatures in the comet cloud to let Eliza talk to them seems like putting the ship in unnecessary danger, something Kirk wouldn't have done just to give a better speech. The threat to the ship is gone, "let's get the hell out of here," is more like it. If you're a Doctor Who fan, it's like when Rory says, "Did he just bring them back? Did he just save the world from aliens and then bring all the aliens back again?"
I think that may be Kirk's stubborn streak. He didn't get through to the father, he 'didn't expect silence', and that was such a blow that he was unable to let it go.