Sarek informed Kirk that he had to bring Spock & Bones to Mt. Seleya, as "... only there, can both find peace." Sarek never once clarifies why Spock's body is required. Nor does he imply that he knows, or believes, that Spock's body lives. It could even give the impression that Sarek simply wants Spock buried on Vulcan. Yes ... it is a major plot hole, however you slice it.There is absolutely no reason for Kirk to want to go to Genesis, he doesn't know that Spock is alive!
But Harve Bennette, who wrote the script, was put into an awkard position, though. On one hand, there's the broken triad of Kirk/Spock/Bones. Without Spock's logic, Kirk is more inclined to follow an irrational course of action. Secondly, this movie is trying to do something that couldn't happen in the series. It's trying to take STAR TREK to a different area of character study and that's to show Kirk & Company having gone rogue. This has never happened, before. And the reason behind it is the bonds of friendship ... of family. We sometimes do things for our family that we'd never do for ourselves.
And when the shit hits the fan, we hope against hope that the impossible can happen, especially when a loved-one's Life is at stake. For all of these reasons, and possibly more, Sarek persuades Kirk to search for Spock. Yes, it would've been nice to have Grissom inform Starfleet that Spock's body lives and bring him back home, but ... all of that popcorn was at stake. So, Harve went for the "it's just a movie" justification and wrote his story, anyway.