A root certificate can be used to issue intermediate certificates.
The private key of the root certificate is needed in order to sign any intermediate certificates.
However, after that, we only need the public key of the root certificate to verify the signature of intermediate certificates.
Similarly, the private key of an intermediate certificate is needed to sign the public keys of SSL certificates issued by it but after that we no longer seem to need the private key of the intermediate certificate for anything other than issuing and signing more SSL certificates.
Does the private key of a CA certificate have any uses other than signing the certificates issued by it?