Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations indicate destructiveHint=true and idempotentHint=true, but the description only states that the course itself isn't deleted. It doesn't disclose that the operation is irreversible for the collection membership, nor does it mention any side effects (e.g., what happens to the collection if it becomes empty) or authorization requirements. With annotations present, the bar is lower, but the description adds little beyond what annotations imply.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.