Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare destructiveHint=true and idempotentHint=true, so the safety profile is covered. The description goes meaningfully beyond that by disclosing the downstream side effect on courses (they fall back to the default design and keep issuing) and a plan-level authorization gate, which an agent could not infer from the annotations or schema.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.