Tested again with different units, me commanding the infantry. Loose formation to present a harder target, and hold fire to reach melee range as quickly as possible. We did better than the AI, but still got murdered.
I also tested with other types of infantry such as Pikemen and got similar results.
Archers are strong against too many types of unit. Even their counter (shield infantry) can be quickly defeated by archers, if there is a small amount of infantry who make the shield infantry drop their shields.
The protection of armour against arrows should increase 1.5-2x, so that it takes an average of 7-8 chest shots for a T5 archer to kill a T5 unit.