Doumo, Yuusha no Chichi desu. 〜Kono Tabi wa Gusoku ga Gomeiwaku wo Kakete, Moushiwake Arimasen〜 - Vol. 2 Ch. 7

[BuyVelomobiles]

Leaving on one's own volition is usually a "want to", not a "need to".

Yeah. She "wants to" leave because everyone is treating her like shit. She doesn't "Need to" leave, because she has the choice to stay. There's no great "need" being addressed here. You can technically phrase "Want" statements as "Need" statements by just setting up the action as the condition for the result, like "She needs to leave if she doesn't want to be treated like shit", but this is just playing semantic games. There's nothing stopping her from staying for the foreseeable future.

And yes, death counts as "not staying", even if her body is left there. It would count as a "Needing to leave", since she wouldn't stay around anyway if she refused. I don't usually feel I have to explain obvious things like that, but I'm sensing you're going to get even more pedantic about this.