I read in a blue post about PvP templates that casters would get a 55% increase in primary stats because they don't benefit from weapon damage.

There are also other classes that don't (or much less) benefit from weapon damage. For example monks; all abilities scale with attack power, and not with weapon damage anymore (changed since Legion pre-patch). So if the item level of the artefact changes throughout Legion (or can be upgraded with those relics?) some classes will fall behind in damage. Casters have been taken care off with the increased stat, but it seems they forgot some classes!

In my opinion Blizzard should make all classes scale with attack power only, and remove the additional increase from the weapon damage.

I tested that assuming the same item level to ensure same attack power, weapon damage does matter for attacks that scale from it. (Tested changing between str/int sword in arena on my prot paladin showing a change in Hammer of the Righteous damage.)