Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnlyHint=false, destructiveHint=false and openWorldHint=true; the description adds value beyond that by disclosing the external side effect ('who gets a push'), which is exactly the kind of real-world consequence an agent needs. It still omits delivery failure behavior, rate limits, or whether messages can be recalled.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.