Do you also ban humans from having Strength 20? After all, a grizzly bear only has Strength 19, and the strongest human that ever lived is nowhere near as strong as a bear.
Strength in 5E, as in 3E, scales by size. A Str 19 Large creature is stronger than a Str 19 Medium creature. If you want to make halflings more realistic, I would simply take the size-related encumbrance modifiers and extend them to cover Small creatures (instead of half encumbrance for Tiny creatures, make it half encumbrance for Small and quarter encumbrance for Tiny).
But be sure to adjust the weight of halfling equipment to match. Halfling armor should weigh 1/4 as much as equivalent human armor.
Strength in 5E, as in 3E, scales by size. A Str 19 Large creature is stronger than a Str 19 Medium creature. If you want to make halflings more realistic, I would simply take the size-related encumbrance modifiers and extend them to cover Small creatures (instead of half encumbrance for Tiny creatures, make it half encumbrance for Small and quarter encumbrance for Tiny).
But be sure to adjust the weight of halfling equipment to match. Halfling armor should weigh 1/4 as much as equivalent human armor.