Hah! For years when I played the piano, I held my hands like I now type; relatively flat fingered and straight wristed. It never affected my ability to play anything complicated and the only real problem was that my piano teacher insisted that this was not the 'correct' way to hold my hands while playing. Never suffered from RSI during the many many hours I've spent at either type of keyboard.

Whenever I try that position, I quickly feel muscle fatigue in my arms from having them suspended in the air for an extended period of time. I think that is why most people don't type in that position mostly.

I might be doing it wrong somehow, but how do you deal with arm fatigue?

A good part of it might be that my upper-arms are essentially straight down, so it's just biceps. Holding your arms out / forward will tire you out, and it's pretty easy to do that in a lot of desks / setups, especially if they're too high. That, and I tend to move around and/or stop and think a lot. In part because I should, in part because otherwise I get stiff. That tendency to not sit still for long has helped in a lot of other ways too, though it makes me hate long drives :|

hmm..I just tried this and I felt that my wrist were nice and relaxed, but my shoulders were not.

Maybe it's just because I'm using a laptop.

You might be sitting too low, and holding your arms up with your shoulders rather than at your elbows. Keeping your shoulders back seems to help too, another of those things that everyone should be doing but few (myself included, the vast majority of the time) actually do.