I never understood the multi-character troubles until now. Things need account wide.

[Seraphor]

I only agree with cash shop items.

Achievements should be tied to the character, because they're mostly character specific.
No point sharing the "Leveled WHM to 80" achievement if that character is only a level 15 CNJ.

Seasonal event items would be tricky, as again they acquired by the character. Yet many seasonal event items end up in the cash shop, which should make them account wide.