Which is almost exactly why WebPKI doesn't want to support such use-cases. Just this EKU change alone demonstrates how it can hinder WebPKI changes.
Certificate:
Data:
Version: 3 (0x2)
Serial Number: 1096750 (0x10bc2e)
Signature Algorithm: sha256WithRSAEncryption
Issuer: C = IL, O = StartCom Ltd., OU = Secure Digital Certificate Signing, CN = StartCom Class 1 Primary Intermediate Server CA
Validity
Not Before: May 27 16:16:59 2015 GMT
Not After : May 28 12:34:54 2016 GMT
Subject: C = DE, CN = chat.yax.im, emailAddress = hostmaster@yax.im
X509v3 extensions:
X509v3 Subject Alternative Name:
DNS:chat.yax.im, DNS:yax.im, xmppAddr:chat.yax.im, dnsSRV:chat.yax.im, xmppAddr:yax.im, dnsSRV:yax.im
Ironically, this was the last server certificate I obtained pre-LetsEncrypt.Last time I checked, Let's Encrypt was saying they provide free TLS certs, not free WebPKI certs. When did that change?
Lets encrypt provides value by providing signed TLS certs that are enrolled in webPKI (i.e. trusted by browsers).
If they were just provided a (not necessarily trusted) tls cert, like what anyone can generate from the command line, nobody would use them.
This is a significant and important use case that's totally ignored by the "WebPKI" proponents, and there is no alternative infrastructure that would provide that value if WebPKI would e.g. decide to add certificate constraints limiting issued certificates to TCP/433.