A federated ecosystem of servers that need to verify each other based on their domain name as the identity is the prime use-case for a public CA to issue domain-verified client certificates. XMPP happens to be this ecosystem.
Rolling out a private PKI for XMPP, with a dedicated Root CA, would be a significant effort, essentially redoing all the hard work of LetsEncrypt, but without the major funding, thus ending up with an insecure solution.
We make use of the public CAs, that have been issuing TLS certificates based on domain validation, for quite a few years now, before the public TLS CAs have been subverted to become public HTTPS-only CAs by Google and the CA/Browser Forum.
> Rolling out a private PKI for XMPP, with a dedicated Root CA, would be a significant effort
Rolling out a change that removes the EKU check would not be that much effort however.