- hit points aren't just luck; the Con bonus indicates they are health/endurance as well. (Not really relevant for me, since I'm ganking the Con bonus...)
- magic-users can do more damage with spells, why limit fighters? (Of course, fighters get to kill multiple 1 HD opponents and survive combats magic-users can't, but let's ignore that...)
The short answer to all of this is "I like what I like", but OK, let's delve into all the myriad reasons why I like it in the first place.
- I prefer ad hoc rulings and improvisation over detailed subsystems and reference materials.
- I prefer abstract principles to concrete simulation.
- I prefer mechanics that make stuff happen to mechanics that "balance" the game or limit unpredictability.
- I prefer a game book that's a training manual and a source of inspiration, a document I need to refer to constantly.
Presumably, people who prefer solid, concrete new D&D over ad hoc, abstract old D&D know what the advantages of variable damage for weapons are. What do I see as the disadvantages?
- It encourages GMs to think of weapon differences in terms of numbers instead of qualities. When interpreting combat, most new school GMs just go with the damage roll and attack mode (melee, ranged, area.) There's not much differentiation aside from that. If weapon effectiveness versus armor type, durability of materials, or other issues besides damage, range, and number of victims is even considered, it's again handled in terms of numbers (the infamous AD&D weapon adjustments for speed and effectiveness against armor type; weapon hit points, etc.)
- It encourages players to choose the optimum (best damage) weapon instead of an interesting one. If all the GM cares about is numbers, that's all the players care about, too. Why would a fighter limit himself to a weapon that does less damage? Why pick a club instead of a sword, even if you have a hankering to play a wildman?
- It encourages a descent into fiddling with "game balance" instead of coming up with new material. To add a new weapon, you have to decide how much damage it's going to do. But wait! What if it weighs less or costs less than an existing weapon? Won't everyone switch to the new weapon? What if it makes a published adventure too easy, because the weapon's high damage lets players kill the orcs too fast? If you want more variability in the choice of weapons, how do you encourage that? Through weapon specialization or feats, of course. Which throws off the game balance again, and you have to beef up the monsters...
- It discourages reuse of existing mechanics. Take "social combat". How much damage does an insult do, compared to revealing a dark secret? If you're going to use the existing combat rules in a "solid" system, you have to set damage types for different kinds of social attack... or just go with "all social attacks do 1d6 damage", but in that case, why not go all the way? Also, your hit point system is balanced for variable weapon damage, with a first level fighter (d8 or d10 for hit dice) being harder to kill than a magic-user (d4). Are fighters harder to insult? Or do you come up with a separate hit point pool for social combat (and psionic combat, and other kinds of combat you choose to add?)
- It discourages thinking of hit points as luck or as an abstract pacing mechanic, as already seen in the preceding social combat example. You start worrying about how much damage a fall off a hundred-foot cliff should do, and whether 9th level characters should be able to walk away from a fall and 1st level characters should be guaranteed death, and how much damage an aimed shot to the head should do. You start tying hit dice for new monsters to size.
Now, do you see why I avoid "I like/hate X" posts? A whole lot of words, no usable content, and that's after deleting some material. Knowing that I like d6-only weapons isn't going to improve anyone's game; everyone, just play the way you prefer, and don't worry about me.