Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnly, idempotent, non-destructive, so the safety profile is covered. The description adds real value beyond that: the deterministic algorithm (so results are verifiable) and the '1 credit' cost, which is operationally relevant. It stops short of stating the return form (boolean) explicitly, though 'Checks if' strongly implies it.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.