Thank you for writing this!
did:key is used as an example in FEP-c390, but this FEP is compatible with all DID methods (even did:plc). For cross-platform logins one can use did:web, which supports key rotation and doesn't require installation of additional software (like blockchain node).
Someone wrote a spec for did:web authentication: https://git.juici.ly/consensual/federated-auth-network/src/branch/master/SPEC.md