I like to give people wins, so I’ll give you this one!
I really do want to back out, and will after this, because my long forum experience tells me that when discussions get too long and too argumentative, they end on a sour note. And I’m trying to not end my discussions on sour notes. It’s annoying. 
Anyway,
I’ll try an analogy.
Let’s say me and my wife have to pick up an infinite number of kids from the school and drive them to our house before we go back to the school to pick up more kids.
Let’s say we drive an old Nissan that has room for 3 kids plus the 2 of us.
Let’s say that each round to pick up 3 kids and drive them to our house and get back to the school to pick up the next batch of kids takes 30 minutes.
Let’s say we have 8 hours to pick up as many kids as we can.
How many kids can Jito and his wife pick up in their old Nissan in 8 hours?
Well, let’s see. That’s 3 kids per 30 minutes, so that’s 6 kids per hour, times 8 is…48!
48 kids!
Now let’s say that the next day Jito and his wife have upgraded their old Nissan to a Ferrari.
It can also hold 3 kids plus the 2 of us.
But the Ferrari is much faster than the old Nissan, so it can do a round in 20 minutes.
So in 8 hours, how many kids can Jito and his wife pick up in the Ferrari?
Well, let’s see. That’s 3 kids per 20 minutes, so that’s 9 kids per hour, times 8 is…72!
72 kids!
The point you’re trying to make is that the way you transport more kids to the house is by getting more cars with more drivers to transport them.
And that is true, that would be the most efficient way.
The point I’m making is that if you improve the vehicle you transport the kids with, then you can also transport more kids, because you’re improving the time factor.
Back to WoW.
The LFG system is effectively just a means of transportation. It puts people into groups and gets them (manually) transported into dungeons.
If you improve the LFG system in any way so that it puts people into groups faster and transports them to dungeons faster, then you get more people into groups OVER TIME.
Time!
Time is the factor you leave out of your analysis, but it’s important. The faster the tanks and healers get into groups and the groups get going, the faster they get through the dungeon and become ready for another group and another dungeon run.
That’s where the efficiency of an automated queue system comes from. And frankly any other improvement you can think of for the LFG system that would speed up the group-making process would work to the same end.
And with that I’m really really done with this discussion. And that’s a promise! 