That's like special weapons only granting powerful bonuses when the player exclusively uses Flat Blade. It's effectively useless.

Like it or not, most pet jobs use their pets as their primary form of damage or utility. Our pets are our equivalent of a melee job's weaponskills. Restricting special properties from pets is identical in every respect to restricting special properties from useful weaponskills. It makes them absolutely useless.

I will not be building an aeonic weapon for my jobs because they receive precisely zero benefit from them in all normal circumstances. That is bad design.

Consider another parallel - special weapons for melee jobs that activate when the user restores another player's HP. I'm sure there are niche uses for small-group messing around, but realistically? Useless, and not what melee jobs signed up for. Bad design. The same design.