Oh lots of people will not be comfortable with tmux approach. The anthropic feature makes sense. But it's Max only and doesn't work well according to other comments.
Ease of setup is the biggest reason. I use this setup as well, but there are other UX niceties that would be a lot better with a dedicated mobile app: push notifications when Claude needs your input (I use a hook for this that connects to Pushover, but that's another service and extra setup), voice input, autocorrect that's right for this context, etc.