This is accurate, but is not the whole story. I’m running a terminal on iOS right now to ssh into my Linux server.[1] There are terminal emulators on Android too.

I wish there were more GUI apps centered around hybrid cloud/shell use cases. I would like to be able to make GUI widgets to do things in a ssh session on my server. I’m not sure how important it would be to run on the device; it could be a webapp I run on the server itself to trigger scripts. It’s a UI/UX that centers around touchscreen input, is reconfigurable, and can perform arbitrary commands or events server-side, which I find lacking. Anyone know of tools that scratch this itch?

[1] https://github.com/ish-app/ish

I ain't sure how "I can run a terminal on a phone" has much to do with "I have full control over the physical machine I paid for and ostensibly own". Unless you're sideloading via jailbreaking (which has a score of problems, not the least of which being that Apple is hell-bent on "fixing" jailbreaks, resulting in a cat-and-mouse game with no end in sight), your ability to run that terminal is exclusively the result of your device's manufacturer explicitly deeming that particular terminal (and the programs it executes) worthy.

Android is slightly better in this regard in the sense that it's (usually) easier to sideload applications, and sometimes even possible to modify or outright replace (most of) the operating system, but this, too, is subject to the whims of manufacturers rather than being something the user (and the user alone) controls.

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On another note, I, too, would be interested in scratching that itch. It seems like it'd be straightforward to throw together.

My understanding is that Android is going to start disallowing execution of downloaded binaries, and they'll need to be in an apps lib folder. See the termux issues on GitHub for a discussion of this.