OK, let's investigate.
Here is a list of letter frequencies including punctuation:
http://mdickens.me/typing/letter_frequency.html
From most common to most rare, this is the order (in English, overall):
SPC e t a o i n s r h l d c u m f g p y w ENT b , . v k - " _ ' x ) ( ; 0 j 1 q = 2 : z / * ! ? $ 3 5 > { } 4 9 [ ] 8 6 7 \ + | & < % @ # ^ ` ~
Note: this does not include keys like Shift, Tab and Backspace. I couldn't find a list that includes everything.
Let's say that in my proposal, the following keys are on the left:
1 2 3 4 5 Q W E R T A S D F G Z X C V
and the following keys are on the right:
7 8 9 0 I O P \ ENT J K L / Tab M , . SPC
(the other keys are in the middle)
In a 'centered' layout, the following keys are on the left:
1 2 3 4 5 Q W E R A S D F , . Z X C
and the following are on the right:
7 8 9 0 U I O P ENT H J K L N M SPC
In my proposal we have (for the 26 most important keys):
SPC e t a o i n s r h l d c u m f g p y w ENT b , . v k
R L L L R R M L L M R L L M R L M R M L R M R R L R
10 times Left, 10 times Right, 6 times Middle
In the 'centered' layout we have:
R L M L R R R L L R R L L R R L M R M L R M L L M R
10 times Left, 11 times Right, 5 times Middle
Not a huge difference. Of course this is just a quick estimate, feel free to improve this analysis.
I think the right thumb pretty much gets enough action in my layout proposal, with Backspace, Enter, Tab, Space, and most punctuation. It's unlikely that you'll be able to do much with just your left thumb.
I think there might be a risk of putting too many important keys to the right. If you would put , and . in their normal spot in the 'centered' layout, it would perhaps be too biased to the right.
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