Landley said in one of his talks (I think it was the linked one) that his goal with Toybox was to enable Android devices to function as a Linux-like development environment.

Toybox provides the shell utilities. You can plug in a keyboard and mouse via the USB charging port. You can screencast to a TV via a Chromecast. Somehow you'd need to get a compilation toolchain on there.

It's an interesting idea IMO. For many people an Android device is their only computer... though I'm not aware of anyone doing this for real in the wild?

To be a little pedantic, that's not exactly what he meant. I only say this because his true vision is a lot more beautiful than that.

He wants to reduce the barrier to entry for tech and empower anyone with the drive to build not be limited by their resources. This is particularly why he focuses on Android smartphones because they're the most popular in the developing world. Also since smartphones are full fledged computers with touchscreens as their primary input method it's the perfect tool for this.

Furthermore, his baseline for this is any such device should have the tools necessary to build a working version of Linux from start to finish on itself. Which is why he's built toy box; it should, by the end of it, have all the tools necessary to building a working build of Linux with a single binary.