...That is why Saavik did not question Spock’s funeral or any other actions Kirk made regarding the death of Spock.
So according to the novelization, Spock did indeed have a will that stated that his remains were not to be returned to Vulcan, and because of that, Kirk intended for Spock’s body to be launched into space and incinerated in the upper atmosphere of the Genesis Planet, not unlike a Viking hero‘s funeral pyre at sea. Gravity was in flux and the coffin-tube soft-landed, unbeknownst to the crew at the time.
There was no “Genesis hope” in either Sarek or Kirk that Spock’s body may have been regenerated. It is made explicitly clear that the deceased body of the Vulcan is necessary for the ritual to transfer the katra from the katra holder to the Hall of Ancient Thought on Vulcan (afterlife), so that and McCoy’s well-being alone are reasons enough to go back to Genesis to retrieve Spock’s dead body.
Sarek had always just assumed Spock would prepare for following all Vulcan death traditions. After Sarek learned the exact language of the Spock’s will from Kirk‘s mind, Sarek is convinced that because Spock was half human, Spock did not believe that he would be able to transfer his katra to another when he wrote the will, but he remained open to the possibility that he may change his mind in the future. That was obviously to suggest that is what ended up happening, that Spock must have changed his mind at the last minute and melded with McCoy.
Sarek speculates that the mind-meld didn’t work perfectly because of multiple possible factors such as Spock is half-human, McCoy is allergic to katras and McCoy is not Vulcan. If it had worked correctly, then Spock’s katra would have clearly explained to McCoy what was going on and that, contrary to the will, they had to keep Spock’s dead body after all. If McCoy had been completely lucid and not acting as fruity as a nut cake, it can then be assumed that Kirk would have believed McCoy, ignored Spock’s will, and sent the body and McCoy to Mt. Seleya on Vulcan so Spock’s katra can hopefully gain Vulcan immortality. (But then of course Spock couldn’t have come back to life so it’s a good thing the katra transfer didn’t work right!)
This also works to explain why McCoy refers to Spock’s body on Genesis and then immediately refers to going to Mt. Seleya on Vulcan. Spock’s katra and McCoy are not clearly communicating with each other due to the problematic katra transfer. Sarek also states that the issue is amplified by the distance between Spock’s katra in McCoy on Earth and Spock’s body on Genesis, furthermore impressing the value of a Vulcan’s body soon after death and McCoy‘s peril.