Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full behavioral burden, and it only implicitly conveys a read-only diagnostic intent via 'check'. It does not state side effects, auth requirements, or latency/rate behavior, but for a trivial ping the implied read-only nature is reasonably clear, especially since an output schema handles return values.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.