Not a bad solution, but I doubt it would be implemented because Bioware will make considerably more people unhappy than happy if they set up a system like this.
It would also in essence make pve much stronger, if your tryhards in your example were full raid pve geared, they would have 0 expertise, sending the other teams expertise to 0. While the tryhards however are in awesome stat pve gear, the facerollers are now in gear with a completely negated stat.
That being said, Expertise is just too damn good. As a mercenary, it gives me Damage, Tankiness, and more healing, all 1 stat. It is laughable how amazing it is.
Really they need to set it up so that it only buffs your primary roll IMO.