How many generals in an army?

[Ludens]

My question now is - Would he still be a carrier of cowardliness?

No.

Gaining bad traits by not fighting very irritating since throwing depleted generals bodyguards into battles is risky. How the hell do you develop them when you can't attach them to infantry units because you don't want them killed so easily.

Killing a few routers should suffice in proving your general's valour. Also, it doesn't matter if you don't do it in every battle.