Some people can't seem to get any gear, some get all the gear in the world. The underlying problem is: you have the same low chance to get gear every week you run. Sometimes you get gear you don't even need and it gets vendored.
Back during Deathwing LFR raids before the loot change, getting geared seemed to be easier. The reason is because (considering you were with a few nice players and not complete jerks) people who had better or equivilent gear could pass or trade to someone who needs it.
Yes this also created drama but as everyone became really geared, it WAS easier for a new person to get gear.
Create an option to pass.
Players that do not need gear from that boss should be able to automatically pass on the loot. When a player passes, the rest of the raid's chances (those who need gear) goes up on the actual roll.
Of course there will need to be an insentive to pass. So give those players who pass more gold (it has to be more than vendor value of the gear for sure) or give them a coin to increase their role chances for on a boss they actually need loot on.
I have read a few suggestions for LFR but I think this one would make almost everyone happy. The result: You stop getting gear you absolutely do not want/need and someone else has a better chance of getting it. You have a better chance of getting the gear you need by other players passing their role if they do not need the gear.
This brings back the idea that when people begin to get geared, other people get gear as well.
Please offer feedback and don't be a troll :)