I think the issue a lot of people are having is that the (widely accepted) fanon that people can't be let out of the birdcage without throwing the whole thing open or involving Cauldron is colliding with the (mostly discredited) fanon that Panacea's considered important enough for her demand to get any response but "fuck you, go away" or at worst "you want to see him? then you can join him in there, you just tried to extort a government official."
They wouldn't Birdcage her, not for that.
In the aftermath of what she did to Vicky, she had to threaten to release metal-eating and plastic-eating plagues before they would
agree to Birdcage her.
Fanon or otherwise, this is a canon quote {from
Interlude 3.x): "I got international attention over it. The healer. The girl who could cure cancer with a touch, make someone ten years younger, regrow lost limbs."
Apparently, even if there are other healers out there (or people with tangential powers that let them heal) no-one is on her level. She has
international recognition of this. She talks about the pressure she's been under for the last two years; that indicates to me that there's no other healers out there willing or able to take up the slack.
She's not
important. People don't ascribe authority to her. She's "the girl who can heal anyone of anything" and they expect her to
keep doing it. Because she's a superhero, and superheroes should do superheroic stuff. Right?
The question is, what happens when the person who's been doing free healing for the last two years, who has healed a few dozen people, saved maybe a dozen lives,
every day for the last couple of years, decides to ... stop?
Think of it as one of those sneaky addictions. The type that you don't notice until you try to wean yourself off of it.
The comfort comes to a sudden, screeching halt.