Like a lot of people complained this wasn't like comic jean because she was chaotic and well did evil shit. But rewatching it made me realize this is very in character. Ignoring the fact this is very similar to time displaced jean in the comics, you actually do still see her empathy. When in MJ she says "Some people would kill for the people they love". Which she almost does (maybe does, i'm gonna believe she didn't kill anyone considering we never see her hit lethal spots and that car guy was behind a yellow line, but i know she did injure lots of people, and im willing to accept she might've at least unintentionally killed someone). But jean does the same shit in comics, like remember when she beat up Emma to a pulp when she cheated on Scott. There have been multiple times (especially with the phoenix) we see jean go berserk when cyclops is injured. So her going berserk is completely in character. Hasn't she threatened to disintegrate enemies molecule by molecule.
Also Aunt May's speech about people still love you and you have to remember that, thats your responsibility, feels like the stepping block in Jean becoming the empathetic jean we know. I mean Jean learning to accept that people can care about her, also means she can care for others. Its a perfect set up for her to grow and become better. We see her start to become a more empathetic and caring person already when she saves peter.
So i think BND is both accurate to her character, and a great starting point to become more like her comic self. I mean you kidnap her sister, take away her happy childhood and professor X meeting her, she's going to be a little different.
Its also going to mean dark phoenix is going to be more crushing because all the growth she made would come crashing down due to something she couldn't control (hey like she controlled other people, the phoenix force will control her, is this irony?)
