I think that a fair compromise would be changing the the system a bit to give "Need" for the gear of your class, but only until you get it for the first time. Once you do, you can never "Need" on it again, whether or not you have it at the time.
The gear and drop system in place is ridiculous due to the options there are not related to actually using it. Desynthesis and turning in for grand company seals is a massive pain due to how there is an unlimited need for that (for those that care about those). Then there is selling for gil (if someone is running the content, they may as well try to get that extra gil) for everyone else. With "Need" button permanently etched on, it's effectively impossible in most parties to get the gear for your off-class. The greed button could as well be dropped completely and the gear could drop randomly to one of the people for which it would be a "Need", not much would change then.
But if there is a "Need" button only until you first obtain it, then you will be able to get it by playing the class certainly. You sell it, turn in for seals or anything else?! Well, you can still get more, but only with greed, as that's basically what the second copy is. If you no longer have it when you did before, then you clearly don't need it anymore. This would solve the issue pretty much completely while still allow people to be "polite" by playing with their best class and still roll on the gear with a chance of getting it.