I don't think it would be that hot of an idea, not that it couldn't be done.
Basically all of the software will be using the keyboard because it is there. There will be Messaging and note taking apps, not to mention the ported software that expects a keyboard and the emulators for systems like the C64 and Atari800 that need a keyboard very badly.
If you cut the keyboard you lose its functionality, on screen is a lousy way to keyboard. Next you lose the clamshell, so you need to carry it in a case anyway. Thus it isn't smaller, and to properly use it you need to carry a thumb kwyboard.
Since this is all available onboard I don't see the point.
On the other hand, if you are talking about a form factor (and are prepared to accept a keyboard), I can say that a "normal" handheld form factor might look pretty sweet, but I don't see how to do it other than making it look like the XGP or that cell-phone that also looks almost identical.
Trade-offs? It will be much larger and bulkier, it will be more fragile, it will be quite a bit more expensive to achieve the same level of quality.
It sounds good, but the reality seems a little lousy. I think that if you had the pandora in your hands the wish for a different form would evaporate, it seems to be an awesome handheld any way I look at it. It just seems hard for people to actually visualize what it will be like to hold. I know that the PSP let me down horribly, it was such a bad design (so there is a "lite" model now, whatever), so I don't think that this can possibly be as bad as the psp with its horrid controls and metal frame for the optical drive, what were they thinking?