It's awefully complicated, to be so simple. ;-)
The best answer I can come up with is, (the arbitrary 2") above center orientation is an artifact of the engineering influences in the early 20th century (Hickman, Nagler, Klopsteg), promoted and made possible by the use of modern materials which immediately followed.
Wrt to the physics, one must consider the role of string angle. For a demonatration, fold your fave bow string in half, then note the location of center in relation to your nock point. Positive tiller's purpose is to offset this inherent asymetry, of drawing the arrow, necessarily, above the fulcum of the bow hand, also most frequently above dimensional center of the bow.
What I've determined is you can "time" a bow regardless, within reason, of the relative lenghts of the two limbs. I personally value having the arrow pass closer to center, because I can find no justification for handicapping the upper limb by making it both shorter, and necessarily weaker, which puts it doubly at a disadvantage to the lower. When building with natural materials, where we tread as close it's elastic threshold as possible (even beyond in most cases), I prefer to not give the lower limb a "free ride."
It's a really, really good question and study of it will reveal many fundamental, and most frequently not appretiated, aspects of the bowyer's craft. That said, I think most bowyers still use trial and error to time their bows, regardless of the predetermined design and geometry.
With a full arc, so called "bendy handle" bow, one really must shoot it according to it's design, that is placing the bow hand fulcrum at the stiffest point along it's lenght regardless of where that point falls. Or risk getting beaten to death by the resulting handshock. And even on stiff handled bows, one risks pulling a limb out of tiller if you shoot it much different than it was designed.
I look at it as a triangle, arrow pass, positive tiller and nock point. The higher the arrow pass, the more tiller required. The more tiller, the higher the nock point. Since there's a lower limit to nock point (below which one risks interference between the arrow and knuckle/arrow rest), the bowyer's task is to put in just enough tiller so nock point can be used to adjust this back out, or in, according to the style (high wrist versus heeling, three under or split) of the archer. Heeling/split calling for more tiller, and high wrist/three under opposite.
But I'd love to hear my ideas challenged. It's far from resolved in my own thinking, although I've dedicated a great deal of thought, research and experimentation to the subject.
