Wait what since when is Alice a coward. I thought she was a shut in who doesn't like people very much and gets into fights with Marisa a lot.
It was stated outright in her IaMP profile: "Her personality is uncaring towards others, and tends to be obsessed with magic. She pretends that she has a strong attitude, but actually she is kind of a coward in her heart."
PCB also has this: "Dominating the enemy with overwhelming power is not fun at all for Alice, so she always sees her opponent's reaction and tries to fight with power that exceeds the opponent by a hair. Even if she loses, she doesn't show her full power. That's because she thinks it would be the end of the rope for her if she lost with full power."
What's funny is that when people started getting fed up with stuttering tsundere fanon Alice, there was sort of a reactionary "CANON ALICE IS AN ICY BADASS WHO DOESN'T TAKE SHIT FROM ANYONE" which is even MORE wrong. Alice is very insecure :V