Everybody knows the story of the "Alternative" combat system in the LBB's and how it became "the" combat system. I was pondering how that came about. Chainmail's man-to-man system is serviceable enough. It definitely requires some thought on applying it to the dungeon crawl style of D&D play (as opposed to Chainmail's mass combat focus), but at its core it is pretty solid.
Damaging an opponent is based on two factors: weapon wielded and armor worn. Greater skilled was modeled by giving higher level characters more "to-hit" rolls. Personally, I don't view that as multiple attacks. It was established from an early time that there is a lot of give-and-take in a D&D combat round. A single "to-hit" roll actually represented the opportunity to cause damage, rather than a single swing of a weapon. Under the Chainmail system, a more capable fighter will create/find/take advantage of more opportunities to damage an opponent, thus the greater number of "to-hit" rolls allowed. Sure, it's more dice rolling, but if dice rolling is a problem, check this out.
I'm not going to pretend to know the thought processes that went into forging D&D from the raw ore of Chainmail's Fantasy Supplement. I will, however, make my guesses about some of them. I believe that Gary assumed that most of the purchasers/players of D&D would arrive by way of Chainmail, thus having ready access and understanding of that volumes combat rules. That simple assumption freed them from the necessity of including all of Chainmail's man-to-man and fantasy rules and tables. This is further born out by many of the monster descriptions including some variation of the phrase "otherwise as in the Chainmail rules" and numerous references to Chainmail's troop types (light horse, medium foot, etc). Acknowledging the fact that not all potential D&D buyers would own Chainmail, they included the "alternative combat system", so that the game would still be playable.
It must be remembered that this was during the formative years of the industry of our hobby. Distribution wasn't as wide-spread as today. This wasn't simply the latest role playing title, it was the only role playing title. There weren't stores built on a foundation of RPGs in those days. For many of us the only way to get the game was mail order (or "xerox", or for the truly desperate hand copy), and that took time. No new D&D player who wanted to get started groping through black pits or slaying dragons wanted to wait two months for another book detailing combat, especially when there was an alternative right there in the book.
The rest, as they say, is history. The "alternative combat system" was fleshed out and fully realized in Supplement I: Greyhawk. Part of this involved variable weapon damage and specific hit die types for character classes. I have my suspicions that part of the motivation for that may have been dice sales, since outlets for specialty dice were as rare as hen's teeth (I myself mail ordered dice, as well as Supplement III: Eldritch Wizardry), but that is another topic for another time.