here are some different ones and the traditional bow, notice the bottom third is where the pull is, I read that's when on horse back, why didn't they just make a shorter bow.
The bows were made that way for a number of reasons. While the hand position (relative to the length of the bow) would indeed make it easier for a horseman (or a person kneeling) to shoot the bow, that is not the primary reason for it.
Japanese asymmetrical bows actually have purpose and logic behind them (no surprise).
1. Longevity. A shorter bow is subjected to much more stress and more apt to fail/break, not something you want to happen.
2. A short bow (drawn to the same length) will cause the string to create a much more acute angle. Traditionally the Japanese archer pulls the string back by hooking ir with their thumb. The more acute the angle of the string, the more 'pinch' is created and it becomes more difficult to achieve a good release.
3. Vibration (hand shock). By grasping the bow where they do and 'tillering' both limbs a certain way...you can find a 'node' point where the harmonics are the least disruptive. Careful tillering can produce the same force/draw curve for each limb (if desired) so achieving balance in the middle is not required.
4. A longer bow generally will not 'stack' as quickly as a shorter one.
For the purposes of warfare from horseback...it is not a design I would pick, but they did have their reasons for making the bows the way they did.