I've found the pen to be the one part of my Surface that I don't use all, maybe it's because I am left handed and it leaves OneNote registering a ton of false navigation gestures but it's basically unusable for me.

Overall, I still like my Surface (non Pro) but it's mostly for web browsing and media consumption.

I've heard [1] that you can go into Device settings for the pen/handwriting-recognition and set it to left handed and it will get better at ignoring the touches from your hand to the left of the pen.

[1] Not left handed myself.

Just verified this on the 1st gen Surface Pro I've got here at work. Hit the Win key, type "pen", open "pen settings" and the three basic options are "choose which hand you write with", "show visual effects", and "show cursor".

I'm not left handed so I can't comment on efficacy but the option is indeed there.

I am surprised it does not come with a "left handed" setting! (Even if not two pen container compartments)

There is a setting for handedness in Windows (or at least there was in Windows 7). The most visible change was that context menus appeared on the other side (so that they don't appear under the hand). But if there is some kind of disabled touch zone near the stylus pointer it may be that it's in the direction of the hand as well.

It does. Hit the Windows button and type "pen" and go to "pen settings" and you can change it there.