Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnlyHint=true and destructiveHint=false, so "changes nothing" is largely redundant. The description does add real value beyond the annotations, though: it discloses that both apex and www are checked and that the response reports free/attached/erroring state plus required DNS records.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.