In AD&D, Gnomes, which are only a little bigger than Halflings, do not have a Strength penalty. In 1e, their maximum Strength was 18/50. In 2e, it was 18/00.
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1e Ogres didn't even have 18/00 Strength either
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Though in the Complete Book of Humanoids, a PC Ogre could have 20 Strength.
Now, if AD&D was meant to simulate our real-world physics, it seems odd, doesn't it? There's no explanation for super strong Gnomes, yet they existed in the PHB. Yet I never heard anyone arguing about Gnomes being "unrealistic" or somehow verisimiltude-breaking. It's always the Halflings.
And it's hard to argue that this was a mistake, as Gnomes being nearly as to as strong as Humans persisted for two editions; it wasn't until WotC came in and decided Small creatures should have -2 Strength...
Oh but wait. They didn't decide that. Actually, Small creatures, by the monster rules, have
-4 Strength compared to Medium ones! You can see this with Kobolds in 3e. Which means that, actually, 3e Halflings and Gnomes have
+2 Strength, modified for their size!
D&D physics aren't our physics. There's a lot of examples. I'm not going to dictate how someone wants to play the game, or tell them what their preferences are. You want Halflings to be unable to be played at your tables or have harsh limitations, have at it! And have fun!
But let's not say this is about how realistic the game should be, when D&D has rarely been realistic about this topic. Gnomes and Halflings are either A) much stronger than their size would indicate or B) the Strength score isn't cut and dry about what it means- ie, smaller things should be a lot weaker and bigger things should be a lot stronger, but it was decided to
not be realistic in order to make the game balanced as a game. So you could play a heroic Hobbit and be able to contribute as well as your bigger friends. So an Ogre wouldn't have bonuses to damage that would make it far too threatening to be a early game enemy.
(EDIT: took the word "realism" out of first sentence of last paragraph.)