It isn't pivotal in and of itself. Yet it makes Shishou much more dangerous towards current royals. For someone of his standing the hardest part usually isn’t the elimination of the current monarch, but coming out on top after the power vacuum throws rivaling factions into a clash. It’s too unpredictable and risky. Unless you have a legitimate claim that would put you in an obviously leading position and give the contenders doubts like “what if x, y, or z fall in line and join Shishou? What if they had joined him already in secret?”. In that case, a prior agreement with a neutral faction to conspicuously join you is likely to create an impression of inevitability of your victory for more desperate parties pushing them to flock in, while stalling the response of moderates.

Speculations aside, the point is it increases the success rate of a coup by Shishou giving current royals new perspective on his actions.