Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already cover readOnly/idempotent/non-destructive, and the description adds meaningful behavior beyond them: answers are hidden exactly as for students, diagnostics are not previewable, and it signals low cost ('Cheap'). These are genuine operational facts an agent should know before calling.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.