Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden, and it does disclose two genuinely useful traits the schema cannot: that the result is a live/point-in-time check and that the call is Paid. It also names the return fields (http_status, reachable, latency_ms), which is helpful given there is no output schema. It does not disclose timeouts, redirect handling, or behavior on malformed URLs.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.