Ironically, the princess being swayed by the knights and townsfolk is a perfect example of why she's not fit to lead.
When you're in command, you must be resolute in your authority. Her experienced advisor has stated that they cannot win against such a large force. Yet she allows her knight to inflame the peasants to make a militia, all so that they can fight a battle that most likely won't end in a victory. They just don't want to feel shame. So they're willing to throw villagers to the meat grinder so that they can say. "We tried!" Also, it's not like the bandits are an army trying to invade. They're actively retreating across the border.
As for the "You're dead anyway" argument. They're not. Sure the village is done for, but the peasants can still move on to other villages, get absorbed into their communities.