I can think of a multitude of ways to remove the dominance of psykers without randomizing. Make perils tests on 3d6, problem solved. Goes to roughly 50% chance for a marine psyker.
The majority of reasons that psykers are the default hq is because they're the best or only means of psychic defense. Get psy defense in range of a psyker, and suddenly it becomes close to a 50% probability the power won't go off in the first place.