Because the nimble waif can still carry 300 pounds of gear without breaking a sweat, and manage 600 pounds with difficulty.
A strong but small PC is superheroic
in their realm of expertise. No, it doesn't make sense from a realism point of view, but it fits the fantasy.
When the rules explicitly say "You can do X," and you just choose not to, it's at a bare minimum inelegant. And honestly, to me? It's bad,
generally speaking. Not always, but usually.
Spoiler: An Exception I Can Think Of
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Country Bumpkin Cleric.
Wisdom 20, and so +5 to Insight. No proficiency, because they're a bit naīve, but they've got the raw stats. When the party visits a city, they choose to roll with disadvantage or just outright say "I rolled a 1" without actually rolling when falling for tourist traps.
The reason I'm okay with this? Couple of points, but mainly that this is probably fun for the table. If it's not, then it's worth talking to the player OOC about it, but most tables I've been it will find it funny, believable, and enjoyable.
Notably, this is not a life or death scenario.