Earlier quoted context omitted.
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.
Also I don't see the point of what TLS is supposed to solve here? If you and I (and everyone else) can legitimately get a certificate for 10.0.0.1, then what are you proving exactly over using a self-signed cert? 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.