The comm system isn't to tell you how good you are at the game, it's to bribe people into being somewhat pleasant with each other in duties.
The system works pretty well for that purpose.

But, I'm also in favor of an end-of-instance private review, not as an epeen stroking function, but as a way to signal to players when they may might be missing something with their role. Wildstar had a similar system and it was great. It showed your rank in damage done, healing done, and your skill at surviving, and it allowed for ties. It was all private, and nothing was recorded to your account like a logging system. It was a wonderful replacement for a dps meter (For casual content, more hardcore content did need a bit more info for player improvement.) Just have it be an optional pop up on the side of your screen like loot and comms are. (maybe let you pull it up outside of the instance in your duty tab as well, like have a history of last 3, deleted on logout or something)

I could see rankings for damage (so just a rank for the hp removed from enemies by your character)
Offensive support (the amount of hp you indirectly helped remove from enemies with your damage buffs)
Defensive support (the amount of hp you saved or recovered for your party)
role/job execution (how well you kept your gcd rolling in combat, for healers, avoiding overheals and using dps skills wisely, for tanks how much unavoidable damage they've mitigated.)
Mechanical execution (how well you don't get hit by combat hazards)
And probably a completion time at the very bottom.

And if they REALLY wanna push out the usage of 3rd party apps and websites, give us a little xivanalysis style breakdowns if we click on the individual categories to see what we can correct. (it doesn't need to lay out the entire rotation just things like "this action caused a gcd clip" or "you let your dots fall off here" or "this sequence of spells in this scenario caused overheal" or like in-universe written tips for mechanics if they get failed too much)
'Cause they can ask as nicely as they want for people to not use 3rd party apps to get better, but gamers are very well known for wanting to use tools to get better, and if they're not going to be provided with one (stone sky sea sucks), then they will look elsewhere. And just like XIV does a GREAT job at quelling the use of raid-calling addons, that basically do the fight for you, by having easily readable mechanics and mindfully designed stages, a function like this could do wonders at reducing the amount of people who think they need a dps meter.


And if people are worried about people getting too big for their britches and bragging about their rank/putting down those lower than them after the instance.. well.. that kind of behavior is already not permitted and feel free to block/report :P