It would have been so much better had they used the established "good guy" character of Saavik for that...
I mean, she would still have been automatically more suspect than the main heroes, but at least there would have been some sort of emotional significance to her turning to the dark side.
I would have had saavik turn traitor, but I would have also had Valaris show up as a new character and the new protege of spock and younger than saavik. Both of them would have been on the enterprise, with one setting the other to look like the traitor and the two constantly having a bit of hostility between the two but hiding it in front of spock...
Would have made the enterprise part of the story much more interesting.