Am I missing something here?
This should be a FAQ.
Due to last minute editing, the discovery of Spock's coffin, intact, on Genesis, was made even earlier, and Kirk is actually seen hearing the news. (They had been expecting the tube to perish in orbit.) The finding of Spock's coffin was haunting him, not just Spock's death, as in the re-dubbed voiceover.
But, even as is, it still works.
The novelization goes into more detail about the ritual Sarek wanted for Spock. Significant Vulcans have an opportunity for their katra, or "living spirit", to reside in the Hall of Ancient Thought. When that Vulcan is near death, the katra is passed to another Vulcan, temporarily. Then deceased body and living soul are briefly reunited though a melding ritual and the katra joins the katra collective. Spock's body was irradiated and buried offship, but - had Kirk been the katra carrier, as Sarek assumed - and
a Vulcan carrier would already know, and Kirk was supposed to know, through Spock's katra - to return the body
and soul to Vulcan.
Sarek states, assuming Kirk has the katra, that Spock would have asked Kirk to return his body to Mt Selaya, but "he wouldn't have asked it openly".
When Kirk first encounters McCoy in Spock's quarters, Spock/McCoy tells Kirk to "climb the steps of Mt. Seleya" He never says go to Genesis and pick up Spock's body.
But
Sarek does want the return of the dead body. The meld to McCoy was not fully successful. McCoy was saying to "climb the steps of Mt Selaya", but no one knew why. Sarek would have already been informed of the discovery of Spock's coffin, and now he wants to get the body back for the ritual. But Kirk delares he and Spock couldn't touch at the time of death.
They had no idea that Spock's body had soft landed on the planet and that he was essentially coming back to life.
Exactly, which is why Sarek requests a
different ritual at the end, startling T'Lar. The Fal Tor Pan reunites katra
and a living body, not with the katra community. It was a rare request.
When Sarek visted Kirk and mind melded with him he told Kirk to bring McCoy to Vulcan so both Spock and McCoy would be at peace. He never mentioned anything about going to Genesis. Even if he did how would Sarek know that Spock's body soft landed on Genesis after being shot out from deep space?
David Marcus and Saavik filed a report about the soft-landing (long before investigating and finding baby Spock.) The "by the book" Grissom captain asked Starfleet for permission to beam them down, and told them why. So Sarek was wanting the return of what he assumed was Spock's corpse, still in its photon tube, for the katra ritual.