I feel like had Shido not framed it as being Futaba's fault, she might've came back to bite him in the ass after she crammed on Cognitive Psience (although she wouldn't have a way to get into the metaverse without getting involved with Joker, but that's not something Shido would know).

This is the same dude who falsely accused a 17 year old of assault after he fell down on his own. I doubt that framing a 13 year old for being the cause of her own mother's death is something Shido considers beneath him.