Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple, parameterless health check, the description is complete. It covers the tool's purpose, the conditions under which it should be used (polling from monitoring systems), and its safety profile (no auth, not metered). The annotations already handle the read-only and idempotent aspects. No output schema is present, but for a health check, the return format is likely trivial and not necessary to describe. An agent has all the information needed to invoke it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.