Isn’t what you described exactly what they just released? Now it connects to local Codex and you can pick the model?
Edit: actually it gets worse -- you can't start any tasks any longer in your mobile, you are required to sign in from your desktop/workstation. You can't "sign in" from your CLI.
Whoever made this, paper cuts I wish onto you. It sucks.
Edit2: actually you can ssh, so I presume that allows you to do the CLI -- and you still can do mobile first tasks, but it's not intuitive at all. Mobile first tasks you still can't pick the model, and I haven't tested the workstation connection one. That said, indeed paper cuts.