How did Kirk know he had to steal the Enterprise? Last thing he knew, Spock and his tube were burning up into their component atoms in the upper atmosphere of the Genesis Planet, to the tune of Amazing Grace. As far as Kirk knows, there's no body for him to rescue.
In the novelization, Saavik secretly adjusts the torpedo's orbital parameters to give Spock a soft landing. That's not the case in the movie, since David and the crew of the Grissom are surprised to find the tube on the surface.
The gravitational fields were in flux, David says. That's remarkably fortunate, because otherwise it would have made for an incredibly awkward conversation with Spock's dad.
Of course none of this would have happened in the first place if Chekov knew how to count to six.