Great question Sascha,
I’m pretty sure the answer is just preference.
The thing that you DON’T want though is for the bone to drastically jump when you switch from edit mode to pose mode.
I call this ‘mode shifting’ – which is not an official term. I don’t think it has one, but I think it sounds cool.
Ideally you want it to stay exactly in the same spot but sometimes that isn’t possible.
Small shift is fine, large shift is not.
As to why it points to the X axis – I’m not actually sure. Maybe that was just chosen arbitrarily by Ton 30 something years ago?
Logically it makes sense because it’s the first axis.
But technically the Z axis makes more sense because when a bone is symmetrized, the Z axis is the horizontal mirror across the X (pose space).
Where as the X axis does not. (it mirrors on the z)