Halflings can be quite fun to play, but you are right - they are seldom the star of the show. The ability to literally save others lives in the party by being a good luck charm is extremely rewarding, though. No, they are not great hand to hand specialists like warriors and dwarves, or even as good as clerics and thieves, but then again they probably shouldn't be since they have other abilities. You are looking at game balance in terms of damage productivity, but the idea, I think, is more about balance of fun and making each class unique in their own ways. They also seem to be quite a bit more survivable than they appear on paper, at least partly because the rest of the party loves to help them stay alive whenever they can. .
Surely some good points and the burly Warrior bellowing “Get your hands of our lucky charm” is enough to warm the cockles of any Hairyfoot.
But I guess if you simply MUST reduce it all to a spreadsheet, then there are a couple other minor things that it occurs to me that you should probably factor into your equation. First, they also have the advantages of infravision and the demi-human saving throws over the warrior, cleric, thief and wizard. Second, they are more likely to score a critical hit, even moreso than warriors. Halfling crit chance per round is 12.5% (with about 0.4% chance of scoring two crits), warrior chance is 10% per round and everyone else has a 5% chance. They also have the ability to fit into small places. I have no idea how you could quantify that, but unless the character is playing an adventure that is nothing but combat encounter after combat encounter, this could be another advantage. .
Yes I get the numbers although it’s not just about how often you critical but what dice and which table you are rolling on and yes they have 2nd rate infravision and good saving throws; it’s just not enough IMHO
Lastly, I would have to disagree with your assessment of the potential downfall of having no benefit for the two weapon fighting (because the character has a 16+ dex), or an ineffective Good Luck Charm because they have a poor Luck score. These are potential problems for all characters, especially the three demi-humans. The chances are the same that you end up with a dwarf who has poor Strength and/or Stamina, or greater that you have an elf with poor Strength and/or Intelligence and/or Stamina. In the end, I think it's a wash for all the demi-humans in this respect, and slightly better for the human classes (since you have the flexibility to choose something that caters to your character's scores).
Yes all characters are subject to fate concerning die rolls and the fact this is more impactive to Demi-Human’s is a great feature of the game but it doesn’t affect all classes the same.
Whatever stats a Dwarf has the advantages of Sword & Board will be the same; by comparison the marginal advantage gained by a Halfling for Two Weapon fighting is variable depending on his agility because what is does is grant an effect based on a certain ability which Sword and board does not.