OK, that's two different issues there:
1. Sitting posture. If you sit at the computer like a statue all day long, you WILL have problems - that should be common knowledge these days.
2. Typing technique. Obviously the process of typing on a keyboard or originally typewriter is much different from writing by hand.
The latter requires very precise hand movements and quite a bit of concentration to create the desired lines in a small area. (Speaking of which, consider yourself glad that you don't have to decipher my handwriting here...
) There are some people who can write with two hands at once,
different things no less, but they are not a majority.
An array of keys invites using multiple fingers to hit them, and, once the array exceeds a certain size, using both hands. It is insightful to compare typical input patterns on a cellphone keyboard (ever seen people text using two thumbs? quite interesting, that), a numeric keypad and an alphanumeric keyboard.
In this context, it may be interesting to notice that as much as usage patterns influence design, existing designs also influence usage patterns (humans are highly adaptive after all), i.e. we have feedback going on here - part of why ergonomics is a bit of a "soft" science.
That in turn leads us to the question of why we'd stick to our accustomed - usually two-handed - typing technique even if it may be needlessly fast and detrimental with regard to pointing device usage: Humans may be highly adaptive, but they usually can't learn a new typing technique that quickly (and that's what your suggestion would amount to). If you have to give up muscle memory and explicitly concentrate on writing, it
entirely defeats the purpose of the exercise.
While I personally can type entirely left-handed if needed, there are some things which are just a lot more comfortable when using both hands, particularly when modifiers are involved.
But let's go back to the original motivation: Freeing up one hand. Why do we want to do that? Clearly it would be for pointing device usage. And why is that? Well, typically a keyboard-mouse change incurs a
high penalty for the right hand, assuming the mouse is to the right of the keyboard. From regular home position, the mouse is a looong way off when using a regular fullsize keyboard, usually requiring reorientation upon a change. That's part of why we're after tenkeyless boards here.