Why an entire new root? Perhaps set up a ACME profile [1] where the requestor could ask for clientAuth if their use case would be helped; the default would be off.
Google would be free to reject with-clientAuth HTTPS server certificates in their browser, but why should they care if a XMPP or SMTP server has a such a certificate if the browser never sees it?
[1] https://datatracker.ietf.org/doc/draft-ietf-acme-profiles/