It's been mentioned before and it seems to be true--
the roles of Reliant and Grisson should have been reversed in the films.
Before the Genesis Planet existed, when it was a matter of scouting out potential planet test sites, the Grissom would have been the better choice. No sensitive materials, no security risks. Just scouting out possible planets for a test site.
Afterwards, the Genesis Planet is created. Science investigation is in order yes, but also security and quarantine measures--a job better suited for the Reliant.
All I can think is Morrow was right about Genesis being a galactic controversy and a sensitive subject. Perhaps the appearance of an armed ship like the Reliant would have inflamed those proclaiming the Genesis Project a military weapon. Perhaps Grissom was specifically assigned the mission to show that Genesis was intended as strictly scientific. Or something.