You forget for a nation not truly engaged in a life or death struggle, winning a war is just a method towards much more overarching aim. It is not the overarching or ultimate aim in itself. Therefore winning the war in the quickest way is not necessarily conducive to achieving the more overarching national aim.
For the US, the overarching aim is of course to ensure the security of united states and safeguard her hegemonic position in the world for as long as possible. Using nuclear weapons to win discretionary wars of limited significance encourages many more nations to regard it is vital for their own security to deter the united states with their own nuclear weapons. This would defeat the ultimate aim of the US by bring forward the day when American hegemony would be checkmated by a plethora of semi-friendly or unfriendly Nuevo-nuclear powers.
For the US, the overarching aim is of course to ensure the security of united states and safeguard her hegemonic position in the world for as long as possible. Using nuclear weapons to win discretionary wars of limited significance encourages many more nations to regard it is vital for their own security to deter the united states with their own nuclear weapons. This would defeat the ultimate aim of the US by bring forward the day when American hegemony would be checkmated by a plethora of semi-friendly or unfriendly Nuevo-nuclear powers.
