@ everyone asking why 12 didn’t give the medical kit thingy to Clara… remember Clara saying last series that she doesn’t want to be the last of her kind? Clara doesn’t want to be immortal.
yep. and the reason she didn’t want to be saved in ItFotN is because she saw his own life and didn’t want it. the adventure with him, yes, but not the loneliness. it’s clear immortality is a burden on him, and almost as soon as he saves Ashildr he begins to regret it because he thinks he’s burdened her too. from that final scene, watching Ashildr go from happy to despairing as the world changes around her, it seems there’s a sense of burden in her as well.
plus there’s that moment in the last story, where Clara flat out tells him she doesn’t want to outlive him, that she can’t handle it. he can, in his own way, or at least he thinks he can cope a little better than her because he’s been through it so many times. (maybe he can’t, not really, but he thinks he can. and he’s willing to shoulder that burden if it means Clara doesn’t have to.) at any rate, chances are if they lived forever, she’d meet–for example–another person like Danny. and then he or she would die too, leaving Clara mourning, and it’d keep happening.
they’ve not set immortality up as a good thing, whether it’s with the Doctor, Ashildr, or characters like Captain Jack, and the Dr can take his knowledge of what it feels like, add in his knowledge of what Clara doesn’t want, and come to the conclusion that shoving alien tech in her to make her functionally immortal would be an awful thing to do.