I have one that just aggravates me because it could have been great. Edelgard from Fire Emblem: 3 Houses has a great backstory on paper, but the game does nothing to use it.
Quick explanation of her backstory; Edelgard and her siblings were all tortured by her uncle Arundel/Thales to give them an extra crest and only she survived. This made Edelgard hate crests and wish to erase the nobility to make crests irrelevant. On paper this is great. It gives Edelgard a reason to try and rule Foldan. She blames the church for the creation of them, and since the Kingdom and Alliance work with the Church, this makes them enemies as well.
However, outside of her supports with Byleth and maybe Lysisthea, she never mentions her story to anyone. She has no confrontation with Thales and TWISTD, who are really the only people to blame, and she does not show that her backstory influenced her motivation to anyone other than Byleth. Unlike Dimitri and even Rhea to an extent, we never get to live through her story and her backstory only is there to make her more tragic.
Don't get me wrong, I really like Edelgard. She serves as a very interesting and unique antagonist, especially in the Blue Lions route. But her backstory really needed some work. All that needed to happen is simply to add a fight with Thales and have her address her tragedy. But in the end, I feel like this felt less like "that is very tragic" and just "oh, so that happened". She probably has my least favourite backstory of any villain.