Put the game's most amazing tank, the most amazing DD and a mob to hit in a room - If the DD doesn't hold back, and uses no hate management tools, they are going to pull hate.. Regardless of the tank's gear / skill.
Enmity gear is nice to buffer those situations (especially on fights such as Chimera where melee damage is useless, ie the tank is relying on Enmity tools + ENM gear)...
Not to mention, every well geared job has multiple gear sets with a heavier weight on certain stats in certain situations - not just a tank..
A DD needs heavier accuracy for Garuda / IE, they can choose to go for a full stat cap / attack build or a crit hit rate/power build.
A WHM can go for a VIT / HP set, MND/HPot, or a nuke set..
BLM can build an AMP, INT or ACC set - and have all those to take into account most fights anyway.
Each job has certain situations where weighing in on a certain stat is more effective, and anyone with decent gear / player skill will know this.. As said previously it's all about~ Balance.
You are also basically removing the player's ability/choice to customize their stats to their play style..
On a final note - if you are wearing PVE gear in PVP then I would love to go woop your butt in the PVP arena.