A certain boss has a 50% chance to drop an item (I'm lying, this boss and item does not exist). On the first kill, 50% chance to drop. Second kill 75%, third kill 87.5%, and so on. I lied again. These are the results you get from people who are bad at understanding statistics. It's always a 50% drop, the only change is that with more kills the overall chance for it to have dropped goes up. The dice don't remember and you're never due to see a drop.
But what if they did?
Imagine if the drop rate of an item was based on the number of times you'd killed the boss and not seen the item drop. This would then be averaged across the group, with some exclusions such as ignoring warlocks when calculating the chance of a melee trinket. Also people who have the item would not be counted towards influencing the drop chance.
Currently you make zero progress towards the acquisition of random drops. You're always rolling the same 50% chance. With this change you're at least improving your dice.
Grouping bias: The ideal group would have people who have never seen the item but no longer need it. In other words, you want people who ran a few heroics and then got carried through Naxx, skipping the heroic tier. For people who want an item, it would be beneficial for them to all run together in order to boost the drop chance, but the second someone gets it, you want them out.
Complexity: This is way more complex and therefore more likely to be buggy or prone to exploitation.
Remove the limit on number of drops and instead make all drops based on this system, per person. This means that a raid could see as many as 25 x [number of items each person wants on the loot table] drops. Or zero. On the first run people are likely to see nothing. Bad alternative. :(
Make bosses drop scraps or pieces of drops. These would then be part of various quest chance to forge or in some way create the desired item. This might range in complexity from "collect 4 scraps of lich robes in order to create a [Robe of Awesome] to "obtain these various magical artifacts along with these trade materials and bring them to this hermit crafter, but only after you've sated his thirst for revenge against the evil group that killed his family." Think thunderfury but with a less cool reward and a way higher drop rate (100%).
I realize that neither of my suggestions would be easy to implement and are way too complex. I'm just trying to think of a system that reduces some of the RNG factor in loot, without totally eliminating it It would be a bit boring if bosses dropped nothing but a set number of 'badges' which were then redeemable for any item at that tier of gear.