Worstgen
Johnny B. Decent
Given Robert's apathy to politics, and cold relation to Stannis, someone in the Small Council probably suggested it and he went "Sure, whatever".
ElderOnitar
It was probably initially intended as an honor to Stannis when he first gave it, acknowledging him as heir apparent.
ElderOnitar
OFC, it lost a lot of its prestige when Joffrey and his siblings were born. So Stannis ended up with a less powerful seat than his younger brother.