On top of being a nightmare to code to allow for an extremely large set of variables that might affect how one should score a dungeon/trial, it doesn't solve the problem.

You say the problem is player engagement. Yet your system talks about how well a player performs and not if they are engaged with the game.

This system punishes players who are actively engaged with the game yet do not perform well enough because they are new or for reasons that may be entirely out of their control. Or do not perform well enough according to whatever algorithm is used, but others would say they performed exceptionally well.

The game already has systems in place to deal with leeches who do not engage with the game but want rewards. It's called the kick system. Groups should kick players who are attempting to not help complete the activity.

Players who are actively engaged and learn mechanics get through them quicker. Meaning they can move on to other activities they want to do in the game quicker. Meaning they can progress towards their goals quicker.

Also, it would turn into players running the easiest means to get those medals to accumulate enough of them to get whatever they want unless they make it encounter specific. And if they make it encounter specific, they've got a space issue whether that's UI issue or player's inventory space.