No real reason. You have to start with the decision to orient the Z axis as they did, with Z-up. That betrays an architectural bias: your camera, which everywhere always uses Z as depth, is imagined pointing downward, a birds-eye view, typical to architecture.
But you don’t tend to gives houses armature modifiers. You give characters armature modifiers. And you don’t look at characters from a birds-eye perspective, and the way that their bones are oriented are primarily up down or left right, not in out.
Of course, that doesn’t explain why they chose Y as the “length” vector of a bone instead of Z. Possibly to maintain compatibility with some other standard?
But it really doesn’t matter, and the things you’re complaining about aren’t a big deal to the extent that they make sense.
When you transform a bone, it will act the same in edit and pose mode. The one exception to that is in “local” orientation, where confusingly, local orientation in edit mode uses the local space of the armature, while local space in pose mode uses the local space of the bone. Yes, that was probably a bad idea.
If you want to move a bone in world space axes, use world space. If you want to move it in its local space, use normal space. In either edit or pose mode.
If you want a bone that has the same world space orientation as local space orientation, go into edit mode and rotate it -90 degrees in the X axis.
Would it be better if that orientation was the default new bone? Maybe.
Ideal, to my mind, is to go back to the beginning and question why the birds eye view was adopted as a standard in the first place. It doesn’t matter very much, mostly for viewport orbiting, and it would be nice if orbit poles could be specified in user preferences.