You can issue a TLS certificate with a SAN that is a literal IPv4 address. You do not need a domain to serve TLS to clients. It definitely helps with the UX, but it's not mandatory for the browsers and other web tech to function.

If you're running private PKI, sure, you'll do it.

What value is it when you are behind a proxy that can change IP? I mean, I'm going on the assumption that the proxy is not under his control, nor does it do the tls termination.