Commercially speaking, this is not really viable, because when it comes to a minimal subset of functionality, everyone has his own; therefore, with the exception of extremely minimal devices (and there's plenty on the market - I recently bought one for less than 20$), there's no realistic common denominator.
You can easily see conflicts in the requirements of having it cheap, but at the same time: indestructible touchscreen (costs $$$); long lasting battery (with a powerful enough CPU, it's $$$ again); GPS ($$$); 3G ($$$); super light (regular plastic won't do, therefore: $$$); etc, etc, etc.
The alternative is to have something very cheap and configurable, in other words, something a bit more than minimal. This is not really different from basic Android devices, so you can already get this (as pointed out) installing custom Android versions.
You can easily see conflicts in the requirements of having it cheap, but at the same time: indestructible touchscreen (costs $$$); long lasting battery (with a powerful enough CPU, it's $$$ again); GPS ($$$); 3G ($$$); super light (regular plastic won't do, therefore: $$$); etc, etc, etc.
The alternative is to have something very cheap and configurable, in other words, something a bit more than minimal. This is not really different from basic Android devices, so you can already get this (as pointed out) installing custom Android versions.
Edit: expanded concepts.