You've gotta consider the fact that when they are fighting to the death they are :

1. Routed level of morale (that means if they could run away they would)
If your men are already panicking, then chances are they aren't good for a fight.

2. Surrounded - This means that your men are most likely taking on multiple enemies from various directions. 1v1 is fine and dandy, but a 3v1 fight isn't good.

3 Depleted - Most circumstances (exception militia or vs gunpowder/siege) your units will have a severely reduced number before even getting to that state.


So yeah, add those 3 things together, and despite fighting to the death, they shouldn't be doing much at all.