Two reasons: stability and leverage.
When a person is rigid you can just stick your forearms out and have the person’s back on one arm and the other behind the knees. Think like how hard it is to carry some things far from you with an outstretched arm vs having it close to your body with more leverage available, much easier.
On top of that, limp people would simply slip through your arms, so you have to clasp them as well to add stability, and this increases the muscle load.
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