The math is just aligning it with the Role's purpose.
In a 4 player dungeon under "perfect" conditions:
1 Tank has Enmity 100% of the time
1 Healer does 100% of the healing
2 DPS deals 50%+ of the damage (each responsible for 25%)
In an 8 player dungeon under "perfect" conditions:
2 Tanks have Enmity 100% of the time
2 Healers do 100% healing in tandem with each other
4 DPS deal 50%+ of the damage (each responsible for 12.5%)
In both cases it should be assumed that the Healer does ZERO DPS and thus the DPS players should be able to do 66% of the DPS without an issue if both healers are not doing DPS. In overgeared situations, the Healers may have less need to conserve MP for healing and could probably drive the DPS players portion of DPS down below 50%. So that's when it starts shifting back to the point where a healer may end up doing more DPS than one of the DPS players.
Like what would "improve" the dungeon content management would be to have the dungeon prompt to kick DPS players that can't meet the generous 12.5% or 25% requirement to not be a "lame carry" or kick healers that are spending too much time DPS'ing or attracting enmity with overhealing, or Tanks that are not tanking.
"<Player> DPS is not sufficient to continue the dungeon and will be replaced if the party is KO'd", "<Player>'s healing technique is not sufficient to continue this dungeon and will be replaced upon Party KO", "<Player>'s enmity control is not sufficient to continue this dungeon and will be replaced upon Party KO"
At least that way, it's much easier to get rid of carries, bots, and you don't get situations like what happens in Coil where you wait for 2 hours only to see a vote abandon after the first wipe.
Hence giving a heads-up for the named player to improve or for the rest of the party to be less aggressive on taking other roles (eg Healer tanking, DPS healing, DPS tanking) if they want to keep them.
As for rewarding simply stepping into the encounter room, no if a player can't hit the target, they wouldn't get to "need/greed" on the item, and wouldn't get a clear from such content. For harder "extreme" and "savage" content, the numbers would probably be less generous since they are tuned differently.
Oh my, you have picked an interesting field.
I'd say you're probably only correct about communities that do not have fulltime PvP. So PvE games, yeah, 15% seems pretty consistent.
PvP games, is all about pulling down "white knights" to the bullies level. So games that have a specific PvP element (eg WoW, SW:TOR, Aion, Archeage) where PvP is engaged all the time, players will go out of their way to cause misery to the other faction "because I can." Other games that have PvP as a criminal element instead (Wizardy Online, Archeage), actually creates a community out of the sociopaths and the role players who can keep their moral sense in check to play with them. Like in Wizardy Online... at least the NA version before it was closed, also had a Permadeath mechanic, so it was not in your best interest to keep throwing yourself at someone, because eventually you'll just get ganged up on. Even then, we had at least one "notorious criminal" that everyone had on their personal KOS (Kill on Site) list. Making friends with the players who play criminals, tends to get you a certain level of "Mafia-like" power in that game. I think most players went to TESO or LOTR who played it when it shutdown. But it makes for an interesting case study in how the toxicity of the player base combined with a mechanic (full time PvP) that allows it, actually keeps people from enjoying or even trying it.
So a small portion of players willingly drive people from the game through various forms of
griefing
Which comes back to the mods question. Do not, under any circumstances give players tools to enable griefing. Allowing players to see other players DPS other than their own enables such. In another game I played there was this notorious mod that allowed a decimal value of combat power to be displayed in the game where otherwise would show "weak, weaker, strong, very strong" beside the monster or player's name. That unauthorized mod is so notorious that it's claimed to be the sole excuse to install mods/hacks/cheats into the game client. That mod was the equivalent of being able to see the players maximum DPS, even though it had zero bearing on the players actual skill level as it was only a calculation based off their stats and gear equipped. Still, players would use this unauthorized mod to find PvP targets. I even called out people on this by equipping a kind of twinking gear (gear that deliberately changed the combat power to a low value, to change the skill experience gained when fighting weaker monsters) and standing in places that people same-race PvP, and sure enough there will be every half hour or so, people that just come by entirely to score "weak" kills, when I could kill them in one shot with or without the gear.
Fortunately FFXIV doesn't have such a PvP system, but if a "dueling" system ever came out, this is exactly what would happen if too much access is allowed by authorized mods.