I mean if it's not routable how do you want to prove ownership in a way nobody else can? Just make a domain name.
There would be no way of determining that I can connecting to my-organisation's 10.0.0.1 and not bad-org's 10.0.0.1.
ie. https://10.0.0.1(af81afa8394fd7aa)/index.htm
The identifier would be generated by the certificate authority upon your first request for a certificate, and every time you renew you get to keep the same one.