If you want to experiment with this today, the Google Nexus 7 is relatively hacker-friendly, and inexpensive. Hopefully, this year the first Tizen devices will be launched, and they should be closer to the "white box" we want. Also devices running Firefox "OS" could turn out to be easier to modify. I have no idea whether Intel-based tablets could be made to run PC-based systems like Knoppix unmodified, all adaptations I have looked into, have been based on Debian compiled for ARM. Tried running Debian under/with Android on a rooted, but otherwise unmodified Nexus 7, but I consider that verison mostly as proof of concept: Had to use vncviewer on the tablet for graphics display, for example.

But, as I have written elsewhere here, I think Knoppix on tablets would be a very efficient way of running Linux on them. And most of the needed programs are already up and running there, thanks to the Debian port to ARM.