As I do dungeons, trials, raids, and anything to deal with cooperative teamwork should be heavily change with its commendation system. First, I seen Healers do real foolish gameplay by either damage per second with Holy spam & little effort to heal
Healers dps in uptime when heals arent needed or the damage incoming isnt that bad, many classes have their own heals ( Second wind, Thrill of Battle etc ) and are expected to use them. The dps job is also to stay out of aoes and avoid damage to reduce healing required. Holy is , along with Glare and Dia, very useful, healers are expected to dps when possible.

Tanks not popping their cooldown & not being stationary at times
Tank or not, a tanks job is to still get out of avoidable damage, and to not expect a healer to heal damage they should not be taking. When a boss drops a frontal cone aoe, a tank will sidestep it and then move back. Tanks do not stand still the entire time.

(although the WHM ruins the stun timing for them), and some DPS not pull l their weight with damage.
Unless you are running a parser, you cant know that.

Third, a "Score Activity Performance" of some sort would do well for a system to notice the players role and depending how well the player does in the cooperative dungeon, raid, trial, etc . . . . At the end, it will determine the performance on the party & how each did.
Publically? NO. Absolutely not. Open to misuse and abuse.

Over all, would it favor in rewards to those that did perform their role? Yes, and why? To push players to actually play the role that they select to choose and is it harsh? No, because no one wants to waste their time on trolls or people being stubborn to really understand a role on what it should be, therefore why reward the sorry poorly skilled player base, than the ones that do perform their best? This is my opinion and fair believe on tbe outcome of what I just typed out.
A flat no.