pouch, hold, content, insufficient, put in mouth
嗛 centers on holding or containing something in the mouth, like a pouch or cheek, and by extension being content or satisfied. The sense of insufficiency likely comes from the idea of holding back or being modest, while putting in mouth is the direct physical action.
嗛 combines 口 (mouth) with 兼, which likely contributes the sound and the idea of holding or combining. The exact historical development is uncertain.
The mouth 口 holds something together 兼, like a pouch in the cheek. Picture a hamster stuffing its mouth with seeds, content and full.
For ケン, imagine a contented Ken holding a pouch in his mouth: Ken -> ケン, and he looks satisfied.