The primary reason Sergeants were issued spontoons was not for use in battle. The spontoon is first and foremost a signalling weapon. It's length and the fact that it is easily distinguished from all other weapons carried in the battalion makes it easy to recognize and follow. Added to this, its length means that commands issued with it can more easily be seen by all soldiers of the battalion.

The spontoon is still used today by the US Army Old Guard Fife and Drum Corps which, while they may not use British army Napoleonic war commands, still do use spontoon commands. The point (no pun intended) of a spontoon can be seen here, it remains easily visible from the ear ranks when a battalion is marching in formation.

Sergeants charged with protecting the regimental colors carried spontoons for several reasons:

• As /u/superplaner mentioned, it's a signal-giving device. Certainly not better than a trumpet, flag, drum, or clear command, but very visible when held high. It also serves as a badge of office, like the sash most sergeants would wear.

• It frees a sergeant from the labor-intensive task of loading and firing a musket, keeping him one step detached from the fight, able to watch the situation, look for orders from superiors, and direct his subordinates.

• Should the enemy close and threaten the colors (or colours, since this is a British sergeant), the spontoon is a better dedicated melee weapon than the musket. It's a last-ditch attempt to keep the enemy away from the standard bearers and the standards themselves. A musket with a bayonet is not an awful melee weapon, but the spontoon is much better suited for the role.