Fixing Player engagement DEV pls consider

[Vyrerus]

What's to stop people from taking screenshots of all of their golds, and then other people putting things up in PF like, "Gold medal earners only." for extremes or anything prebuilt?

As far as an actual scoring system goes, they have a scoring system in XIV in the Masked Carnivale. A lot of the points categories are weird and only something relevant to soloing, like, "Taking a Walk" or whatever the one is, that you get for kiting a monster around the arena perimeter once.

If they were going to implement a medal system, it's likely they'd have a scoring system for each job or role at a minimum. It's just, a lot of it would be stuff you'd have to go out of your way for, or it would be stuff that happened so readily, that it becomes meaningless.

I'll also echo other posters responding to the OP in that, you're stating the problem is engagement. There are tons of people who play FFXIV who are fully engaged, but they have stupid hands. They know what they need to do for their rotation, but can't execute it flawlessly or even nearly flawlessly. Others have cement minds. They like to play multiple jobs, but only one or two really click with them, and most of their muscle memory/rotation memory/setup is devoted to their, "Main" job. Implementing ranking in content will drive up the problems with less tanks/less healers even farther, because people willing to step out of their DPS comfort zone to try them will be met with being reminded that they aren't good at them.

[CKNovel]

What's to stop people from taking screenshots of all of their golds, and then other people putting things up in PF like, "Gold medal earners only." for extremes or anything prebuilt?

Photoshop exist. Paint 3D will be enough. A screenshot of "gold medal" isn't enough.

Also, for the idea, I wouldn't do it the way OP posted but at the end of bosses from trials/raid, you'd get an analysis of your performances.
The game would point out things like "You forgot your defensive CD and you went down to XXX HP/KO'd you!" or "Your gauge was overcapping by XXX amount!" or "Use this action on CD!"/"You missed X GCDs in the wildfire window!"
Problem with that, SQEX actually needs to figure how rotations works, their guide and BRD quadweave weren't the greatest documentation.

Score/medals, I don't think they are usefull. A single "You forgot X that could greatly help to improve your performances" would be enough to motivate many.