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My take on it: The rules are written with human(oid)s PCs in mind. Since the races that PCs can be pretty much all have hands, that's what somatic components for PCs are assumed to use.
Somatic components for races that don't have hands but cast spells anyway use gestures appropriate for the creature. When polymorphing (or otherwise changing shape), you need appendages similar enough to what you normally have to perform the somatic components correctly, or you need some ability that allows you to use other gestures, such as the Natural Spell feat.
...Which is pretty similar to what you said in your last paragraph, which I would have noticed if I'd finished reading your post BEFORE writing mine. 8^)