Well, the assignment of sergeants to such roles may be a little limiting, but is certainly grounded in reality. They wouldn't have been only spearmen or medium cavalry, just as knights weren't all swordsmen or Welsh irregulars only equipped with long knives.

Sergeants were basically non-noble professional soldiers (or at least as close to a professional as existed at the time). They were the next level of quality below knights and squires, and played a major role in some battles, making it into accounts such as that of Bouvines in 1214. Their role as mounted sergeants in the game is very satisfactory to me. As infantry, the spear is probably the most reasonable single weapon to give them, though some would likely also have been equipped with swords, maces, axes, polearms, etc.

Ajax