The main advantage is that of having characters where you expect them to be. As you suspect, touch typing doesn't quite work on touch screens - I'm wondering whether something better will surface anytime soon!
I've envisioned having a set of buttons for each finger around the edge of the device for the hand that holds it!, probably including one extra button for the index finger and pinky and 1–2 extra thumb buttons. With those, you could implement all sorts of nice functionality to make your browsing and whatnot way more advanced (akin to keyboard shortcuts alleviating the problems of overmuch mousing), such as forwards/backwards buttons and scrolling with the thumb buttons as accelerators/precision enhancers. And you could type chorded!
For a simple and intuitive chording scheme, imagine the finger buttons corresponding to the buttons on a normal keyboard, and touch screen presses choosing row and mirroring!