Socializing costs and privatizing benefits is a lousy combination.
Many games allow you to increase your difficulty and your reward. This could be explicit in the form of a difficulty dial tied to rewards, but it is more often an opportunity cost. For example, you might equip an item that improves your loot, but doing so forgoes equipping an item that improves your damage. The fight is marginally harder and your rewards are marginally better. Kingdom of Loathing is an example of a game that does both: there are ways to increase monster level, and you can also equip items that have +monster level instead of (or in addition to) stat bonuses.
Kingdom of Loathing is also a single-player game. City of Heroes similarly gives you tools to adjust mission difficulty, and it gives the same difficulty increase and reward increase to everyone.
Multiplayer games that allow individuals to equip +loot items allow those individuals to increase their rewards at a cost of increased difficulty to everyone on the team. Alice is a tank using best-in-slot gear for damage resistance while Bob is a healer using best-in-slot gear for improved loot drops; Alice is working harder and incurring more repair costs for Bob’s benefits. Alice’s only way to avoid players like Bob is to stick with known companions or be That Guy and demand to see your equipment before letting you into the group. If everyone or no one is wearing +loot gear, the situation is fair and both risks and rewards are shared. Allowing individuals to unilaterally increase group difficulty for personal benefit is a solid example of anti-social design.
Doesn’t this lead to the slippery slope of being That Guy and demanding that everyone has a sufficient gearscore? After all, if Cindy has best-in-slot and Dan has whatever quest gear took him to the level cap, Cindy is contributing more and Dan has more room for gain. Yes, but there is a difference between privation and malice. If Dan only has greens, that is all he has to offer; he is doing the best that he can. A group can accept or reject him on that basis, and there is no stigma attached to being the weakest member of a group that accepts you. If Dan only has greens but swaps out his +hp gear for his +loot gear, he is being a leech and a jerk; he could contribute more, but he is actively choosing not to.
(You are also a jerk if you use social pressure to leech. If the group only puts up with it because you are the guild leader’s friend, you are a jerk. If you wait until it is really inconvenient to kick you to solicit “consent,” you are a jerk. There is a stigma attached to being the weasliest member of a group, even if you do not realize that you are a passive-aggressive sociopath.)
You can devise scenarios where having just one or two people in +loot gear instead of contributing fully makes sense. The best gear Edith has found includes some +loot. Frank is playing easier content with friends who all have lousy gear, so he has switched to best-in-slot +loot gear that otherwise has comparable stats to Dan’s gear. Gretta just rejoined the game and her friends are intentionally having her leech in +loot gear so that she can catch up more quickly (indicates other common design problems). Henry is in a MOBA and is being carried through a weak early game to yield a strong late game. The common denominator here is informed consent. No one unilaterally or underhandedly decides that you will work harder so that s/he can gain more.
Unless you are building a game where griefing teammates is a feature rather than a bug, personal loot bonuses are a bad mechanic for multi-player. It encourages anti-social play, which encourages closed social groups, which can lead to strong social bonds but ultimately undermines the playerbase.