So you’re not remapping the source ports to be unique? There’s no mechanism to avoid collisions when multiple clients use the same source port? Full Cone NAT implies that you have to remember the mapping (potentially indefinitely—if you ever reassign a given external IP:port combination to a different internal IP or port after it’s been used you’re not implementing Full Cone NAT), but not that the internal and external ports need to be identical. It would generally only be used when you have a large enough pool of external IP addresses available to assign a unique external IP:port for every internal IP:port. Which usually implies a unique external IP for each internal IP, as you can’t restrict the number of unique ports used by each client. This is why most routers only implement Symmetric NAT.

(If you do have sufficient external IPs the Linux kernel can do Full Cone NAT by translating only the IP addresses and not the ports, via SNAT/DNAT prefix mapping. The part it lacks, for very practical reasons, is support for attempting to create permanent unique mappings from a larger number of unconstrained internal IP:port combinations to a smaller number of external ones.)

Examples of local commands I might run in tmux could include anything long-running which is started from the command line. A virtual machine (qemu), perhaps, or a video encode (ffmpeg). Then if I need to log out or restart my GUI session for any reason—or something goes wrong with the session manager—it won’t take the long-running process with it. While the same could be done with nohup or systemd-run, using tmux allows me to interact with the process after it’s started.

I also have systems which are accessed both locally and remotely, so sometimes (not often) I’ll start a program on a local terminal through tmux so I can later interact with it through SSH without resorting to x11vnc.

Not the GP but I also use tmux (or screen in a pinch) for almost any SSH session, if only as insurance against dropped connections. I occasionally use it for local terminals if there is a chance I might want a command to outlive the current graphical session or migrate to SSH later.

Occasionally it’s nice to be able to control the session from the command line, e.g. splitting a window from a script. I’ve also noticed that wrapping a program in tmux can avoid slowdowns when a command generates a lot of output, depending on the terminal emulator. Some emulators will try to render every update even if it means blocking the output from the program for the GUI to catch up, rather than just updating the state of the terminal in memory and rendering the latest version.