Weirdworld will probably make her a romance option in the future, even though we've had very little of her, she seems like a very good character to me.
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I recommend keeping Jake alive for 2 simple reasons.
1-If you make Mia regain her memory while Jake is dead, she will freak out and run away scared from you. This will surely be a bad thing in the future when the option to have a romance with her becomes available.
2-To just make Jake suffer. In the game it's made very clear that Jake has a huuuuge crush on Mia. To the point of literally mind controlling hundreds of innocent people who had nothing to do with it and ordering them to kill the MC, just so that there's a slim chance of saving her, and all this just because he didn't have the guts to go against ella. So obviously seeing the girl he likes go out and do romantic or sexual things with the guy who kicked his ass is really going to hurt him emotionally >:D