ST III was actually rejiggered very late in the editing process - check out either of the adaptations (comic or novelization) and it's clear the film was meant to lead off with Grissom
arriving at the Genesis planet, then cut to the Enterprise
, back to Genesis, then back to the Enterprise
. That's why the special effect shot of Grissom
has the stardate subtitle -- it was supposed to appear immediately after the opening titles.
I wonder if test audiences were asking who those people were on the Grissom
, leading the studio/producers to decide to lead off with Kirk's log entry. I've always wanted to see that version, to see how it would play.