Couple of problems that I'd see with your suggestion:
1) You'd have to use the stylus in order to activate keys on the eInk side (the eInk screen does not register finger strokes, only those made with the stylus). Personally, I would find that unworkable.
2) Also, based on my experience with the refresh rate of the eInk screen for other functions, it would also likely be unbearably slow.
The onscreen LCD keyboard isn't too bad if you're in landscape mode, although I hate having to hunt-and-peck, so I ordered a folding keyboard to plug in whenever I need to do any sort of prolonged typing.