Ironically, remote work is the main thing I use Claude Desktop (and mobile) for. When I work locally, I’m usually happy with the TUI, unless I need a lot of equations or images. When I work remotely, keeping the SSH connection alive or juggling tmux sessions is too much of a hassle, and running the remote session from Claude Desktop/mobile is more comfortable.
Just a heads up, I build Cosyra, a mobile terminal app, so this problem is something I've been considering a lot. For the SSH side, mosh fixes most of it. And for the tmux sessions I use a leader terminal who does all the juggling for me. Remote control is great, but then I'm completely locked into using Claude which, for me, does not work.
Have you heard about sixel or the kitty graphics protocol? I. what makes me a terminal terrorist, I've got an adaptation of cat on my GitHub where you can cat an image in the terminal, and if you're using a modern terminal, it'll display the graphic.
Claude has a killer feature for me with that remote-control command.
Spawn a Claude TUI where you need it and take remote control with no friction.
I tried it in codex and they messed up the flow so bad. You need to add a device oauth token every time you set it up even though it's already logged into your account.