I'm not really sure what Eve thinks she can go back home to at this point. She doesn't yet know about what happened to Nico's colleague, but she does know that Carolyn's not going to cover for her because Eve chose Villanelle. So assuming she survives that bullet (because of course she will, just as V survived being stabbed), what does she think she can do next? Just go home and pretend nothing happened and that MI6 or Carolyn or the 12 or whoever else won't come after her or hold her responsible for everything that happened?
Frankly, while I understand the logic of not having Eve run off with a potential psychopath, what alternatives do either of them have at this point, if Konstantin and Carolyn won't protect either of them anymore? Shouldn't they both be on the run?
I was kind of ticked at Eve in this final episode, because she gives Villanelle such mixed messages. She touches her face all the time and obsesses about her and runs to save her (leaving poor Hugo to possibly bleed to death!), but when V actually responds to that, Eve keeps pushing her away with disgust as if V is ridiculous to even think that Eve might be attracted to her. What the hell? I'd say she's in some deep denial, or she's being an asshole. Of course she can't get romantically involved with a ruthless killer, but don't lecture Villanelle on needing to be honest and then lie to her about not having any interest or attraction, because that's such bullshit and she knows it and V knows it. Everybody knows it.