I've been roleplaying Miu Iruma a lot in a discord server and hit upon something that, I think, explains a lot about why she's like that. She knows she's a total catch when it comes to her intelligence, skills, and looks. She's also keenly aware that her personality is repulsive.
Why does she care so much about family, to the point of adopting one of those unlovable Monokubs and trying to babytrap Shuichi in the love hotel event? Because people tend to stick with their family, even if they don't like them.
Why does she trick people into eating baked goods with a disturbingly personal touch? She doesn't think anyone would like her enough to want her, even with that body.
Why does she want to save the world with her inventions, despite seeming so selfish and uncaring of other people? Because she wants them to say anything nice about her at the funeral, and there's no guarantee she'll leave a pretty corpse.
Why is her ego like a Thanksgiving parade balloon, so massive in scale yet so easily shot down? Because she knows she sucks.
This makes her fate even more of a bummer. Only a couple of people at the class trial for her murder show any grief. She didn't think people could like her for who she was - only how she looked and what gizmos she made - and she was mostly right.
This is why I like irumatsu so much. Kaede's FTEs see her breaking through Miu's defenses and working hard to be her friend. By the end of their last one, it's working, little by little. And if she'd stayed as protag and Ch 4 proceeded the same way anyway, Kaede would've made sure they all mourned Miu properly.