Hm! I now have a supposition.

If Sakuya doesn't meet Gryphon at this point, his personal future doesn't happen correctly, which results in the Doctor's personal past being altered.

This isn't about not setting something on fire; it's about a paradox that would wreck two dimensions, and probably suck a few more into the chaos.

Peter Eng
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(Also, there's a non-zero probability that if Sakuya doesn't show up when she did, Gryphon gets killed to death in a storm of energy spheres.)