Are bayonet techs critical in early game?

[FactionHeir]

The AI charged my xp2 line infantry with socket bayonets in square mode repeatedly with a single unit of 0xp provincials. I let them be and lost about 37 line before routing the provincials who had 6 men left... Battle Difficulty of M.

Similarly, I lost a lot of Household Cavalry against AI regiment of horse and provincials, which shouldn't be the case especially when they are already more tired to start with and I get the charge in.