I have long been enamored of the d6 HD/d6 weapon damage paradigm. It essentially models the notion that death is always one good damage roll away. Unless, of course, we're talking about higher level characters. Another windmill I have long tilted at is the, in my opinion, lowly state of the fighter. Judging by XP requirements (in the LBB) , fighters should be very stiff competition, ability-wise. Yet, their only benefit that happens automatically is hit points. The other is use of magic swords, which is dependent upon finding a magic sword (of the appropriate alignment).
If you look at Chainmail, you can see that Heroes are forces in a fight, and Superheroes are wrecking balls. They attack as 4 and 8 figures, respectively, against "normal" opponents. Which essentially means that they attack 4 or 8 times against 1HD opponents using the Alternative system. Additionally, under Chainmail, they were considered Fantastic Creatures, and were essentially immune to attack from less than 4 "normal" figures. It's important to note that in Fantastic Combat, a "hit" equals killed.
That is something I have long sought to bring into my D&D, the "lost" abilities of the fighter vs "normal" types. Just giving them multiple attacks didn't fully satisfy, so I kept tinkering and thinking.
At this point, it seems appropriate to mention, I have always been enamored of the elegant simplicity of the LBBs and it is there that I spend most of my time. I have disdained, in my later years at least, such high-falootin' ideas as variable HD and damage. Then, the other day, the subtle genius of E. Gary Gygax finally hit me (again).
If most "normal" types do d6 damage, and a fighter has d8 HP (per Greyhawk), then "normal" types will have to gang up on a Hero to take him down in one round anyway. Just like in Chainmail. And while they are ganged up on him, he'll be attacking them four times per round, or more. When that realization sunk in, I felt like a weight had been lifted.
Sometimes I forget that D&D combat is all about modelling outcomes. It is all about determining who wins the fight. It isn't concerned with who wins individual rounds, that sort of thing exists primarily for entertainment. D&D is about who wins the fight. I'm no statistician, but I have the feeling that the outcome of 4 "normals" ganging up on a Hero in Chainmail, would come pretty close to the outcome of 4 "normals" ganging up on a 4th level fighter from Greyhawk.