The "Why?" is hard to come by.
I've done a few bass bars now, both new and replacements. The way I see it; the centre of the bar is attached to a thickish part of the plate which is the least flexible anyway, so the bar needs not to be flexible right there. So it can remain as thick as I want for weight reasons. However, towards the ends of the bar, the bar needs to flex so as not to restrict the pumping movement of the top, but not so much as to dampen the transmission of string vibrations into the upper and lower bouts. If it was made of rubber, it would do nothing. So its a balance. Right at the ends is where any lifting of the bar may occur, and I'm assuming this is often triggered by a thump on the lower bout, in which the relatively inflexible bar gets cracked away from the moving plate. So the end of the bar is further feathered away to give even more flexibility at that thinnish point of the plate.
I think the shape of the bar must work with the arching shape and the graduations of the top, so there isn't really a formula. Some people "tune" the bar - and certainly Traeger has his methods - but personally i haven't had much success with the process he describes. So the bar taps a tone higher than the plate? What does that mean? So the bar taps the same tone end to end? Is that good? Why?
So I'm going more by the flexibility of the bar itself, and the weight of the bar, and how the outside arching is designed. A long flat arch for example might need extra stiffness in the bar in the middle. I also like the idea of a bit of extra weight under the E foot.
And then there's "how does it look?" because the fairies will see it, and tell on you. Now will i sign the bar, or not??