Rotation limits how much data one key protects and how long a stolen key stays useful. SP 800-57 Part 1 §5.3 gives guidance on cryptoperiods, for example one to three years for a private signature key. Short-lived certificates and tokens shift the problem from rotating keys to renewing credentials automatically.
The pattern is the same across ecosystems: publish the new key, wait until every verifier has it, start signing with it, and retire the old key after everything it signed has expired. JWKS uses kid and cache lifetimes; DKIM uses a new selector; SSH uses UpdateHostKeys to teach clients a new host key; TLS overlaps the old and new certificate; Sigstore and TUF rotate root keys through signed metadata.
Common failures: removing the old key before cached tokens expire, verifiers that fetch keys once at startup, keys without identifiers so verifiers must try them all, and emergency rotations that were never rehearsed.