HI Juju,
I get what you're saying, and for a long time I was always trying to force the Y on bones to be "up".
But now I think about it differently.
Y axis is the length of the bone and then you aim the Z axis in the relevant direction for your model.
When you want to world align a bone - it lays flat.
I used to think it was really weird, but now I like it a lot because I can visually see which bones are world aligned just by looking at them. You don't need to dig into the values to see as they are often perpendicular to the model.
This option might help you if you are importing/exporting from other software.
It doesn't change anything under the hood but it does force the relationship lines to be drawn to the head of the bone.
This will make more sense when working in software that uses 'joints'.
Probably not the answer you were wanting but I hope it does help.
The World Z-Axis is up in Blender, that is just a (more or less) arbitrary decision made one time. There is other Software that uses the Y-Axis up for the World.
An Armature Object, in its default Orientation (as it comes in, when you Add an Armature) is aligned to the World and thus has its Z-Axis up.
A Bone has its Y-Axis along the length of the Bone (from Head to Tail). (I don't know if this is universal, or Software dependent.)
A Mesh Object comes by default in, aligned to the World, so with its Z-Axis up.
A Cube, for instance, (in Edit Mode) has 6 Faces and each Face has its Z-Axis in a different orientation.
Please don't overthink this.
Thank you so much everyone for your kind [and your patience] when explaining, trully appreciated <3