Exactly. My "special case" took a little more care, but it works completely fine. Here's my setup:

1. TCP proxy at edge -> wireguard tunnel using SNI to route to the right service
2. reverse proxy that handles all TLS for all services on its device (renewals and crypto)
3. HTTP services behind a firewall that only communicate w/ proxy

I have my router configured to resolve DNS to #2, so I don't need to hit the WAN to access local services over TLS, and it uses the exact same cert as WAN traffic and the browser is happy.

This is about as exotic as I can think of, and it still works just fine for TLS renewals, and it's 100% automated. I do need to leave HTTP open (it only serves acme endpoints, so whatever), but I could also close that down and have the renewal process open that temporarily if needed.

The only special case I can think of is a device that rarely turns on, which is incredibly rare these days (you'd generally have an always-on gateway that uses self-signed certs or something for those devices that stay off).