You can do both. I often ended up running emacs on a remote server using ssh/tmux as it was easier to keep my state on said server (processes etc) and just reconnect.
Single biggest bugbear for me using emacs over SSH (non-TRAMP, remote-ssh and run emacs --daemon and then emacsclient -t locally on that machine) is on a laptop, I find that the session drops frequently and I need to reconnect (sometimes after hitting return-tilde-dot to unfreeze the dead terminal session). I've never really figured out how to fully stabilize my SSH (and I certainly don't have anything as convenient as "Actually auto-restores the session if it breaks," which is something vscode seems capable of doing for the shells it opens).
Second bugbear is running in terminal so all my GUI conveniences are missing, but it's emacs so that's a distant second to the first.
Sure, but not being able to access your local system with your text editor is a bit strange to me. If you know that you won't need to then there is no problem with that though.
on my current setup, from a thin-client I remote desktop to a windows machine where I vnc to a xvnc linux server, from which I ssh -X to a large shared dev machine. From there I run gui emacs, often using TRAMP to access remote files.
The amazing thing is that this contraption is actually usable.
