I propose two simple changes to circumvent this growing pain which will no doubt inflate in both intensity and irritation. They can either be implemented together or independently. As it stands, the process of LFR loot distribution allows for one roll per week. Originally there was talk about there being eligibility for one piece of loot per boss per week, in so many words. This translates to anyone who has even a remote attachment or relevance to a piece of equipment can roll and receive it over anyone else any time and thus waste yet another entire week of the patient player's time. Why not make this true to the words? Since the LFR is a queue system most commonly approached in solo fashion thrusting the player into an environment of people they have had no previous experience with, it is only fair to allow for some leeway, not to mention fairness.
LFR should be open all week. You should be eligible to roll as many times as possible per week per run until you receive one piece of equipment per boss per week. This will mitigate the absolutely nonsensical lack of justice and fairness when it comes to loot distribution.
In addition, there is another variation that can be applied in tandem to this change. I dub it selective loot table and it executes thusly:
No matter how many pieces of equipment a boss encounter drops, at least one (1) should be selectable. This can be chosen by the loot master or voted on for the sake of fairness. Applying this will reduce the hair-pulling frustration of having repeat loot on the same table every cycle. If an encounter is limited to dropping one piece, so be it. Everyone can vote on what they want independently and it will simply be a useful arbitrary drop.
I recommend, with the utmost of urgency and haste, that this system be implemented. There is no denying it is simple, concise, greatly reduces headaches on both sides of the issue and can be applied with minimal effort. There is virtually no downside, with the possible exception being people will get loot faster and clear content quicker (God forbid people get things done and have more fun).