Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already establish readOnlyHint, idempotentHint and openWorldHint, so the safety profile is covered. The description adds useful behavior of its own: the tool reports live status, URL and domain state, and the usage note makes clear the result is meant as an authoritative liveness check. It doesn't cover failure modes or the shape of the response.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.