I think we're getting a bit sidetracked.
But I also think a really central point may have been over looked. Some one else is calling XVG to come get her. (Right?) Who ever is calling can just as easily call a taxi for her or call community patrol. I'm not sure if every city has one of those. Where I live, it's a city patrol that picks up people 'incapacitated by alcohol' in public places, takes them into protective custody and to a sleep-off center. Not the coolest thing, but then IMO neither is public intoxication.
My number is still in XAH's phone - I know this, because the stupid sh-t keeps texting me 'accidentally' the little love notes he means to send to his GF. If some one were to call me and say XAH is here drunk and keeps saying your name 1. I'd run because well, that just can't be good, and 2. I'd say sorry, I am not involved with him any more. I will not come get him.
My situation is different than yours, XVG. If she is still kind of a friend, one approach may be to tell her, when she's sober (because if she's like XAH, she won't remember it if she's drunk) "I can't help with this any more." It really is more about what feels right for you, XVG. If you feel you should tell her "I'm done picking you up." then it's the right thing for you to do; do it once - for yourself. And if it keeps happening, well, take what ever steps you need to take to enforce your boundary.