Yeah the remote control featureset is pretty limited right now. I did a comparison here https://yepanywhere.com/claude-code-remote-control/ (with my own project). I'm sure they'll iterate on it. Overall it's such an obvious feature for them to add I'm surprised it took them so long to ship. There are probably at least 50 such projects that people have made (https://github.com/kzahel/yepanywhere/blob/main/docs/competi...)
The one feature drawback of tailscale/tmux/termius is no file upload. And ergonomics, ability to view files/diffs easily, though that's subjective.
Perhaps it took a while to figure out how to do it over HTTP, especially the security stuff.
With e.g. tmux you'll piggyback on decades of SSH development.