Makes me wish you could buy a kit and assemble your own phone. We need someone like Arduino to come along for this kind of tech. Would be awesome to just pick up my old and faithful Hakko and solder some sensor to a phone.
Depending on what you're thinking of when you say "phone", you can do that. 3G modem, controller (either a microcontroller like Arduino or one of the smaller Linux-based ARM computers), various LCD options, and either touch or buttons for input. People have built variations on that.
Put a smaller GPIO connection on the screen, and you could probably make it 1/3 the thickness of the original one. Still much more powerful than my first Android phone, and you could set it up with much quicker software. Actually getting to feature parity even with most feature phones would take some serious work, though.