The Return of Nevermore (Part 1) by Morpheus

Involuntary outing is /not cool (tm)/. Not even if it is done by your father, for the greater good.

It does show the problems inherent in a superhero mindset. Or I should say the paragon mindset. The literary paragon, not the Whateley one.
I am borrowing the explanation, and warning, from Overly Sarcastic Productions here. Paragons have a fixed and absolute morality, and cannot be swayed by considerations that any situation is actually morally grey. They 'know' that they are right and they 'know' that they are the ones to act in one specific way to 'right' the situation. Some of the best Superman stories explored this to show how easily this trait can turn from 'the rolemodel who helps everybody and never gives up' to 'the tyrant who suppresses any dissent with an iron fist'

That is not to say that The Face here is anywhere near tyrannical, but he is willing to sacrifice his daughter's safety (and maybe even her mental health) for 'the greater good'. In his mind there is no possibility that his daughter need not be outed as (involuntary) TG, and her opinion is neither relevant nor really sought.

The story itself is of course excellent. It has an Avengers vibe to it where individual heroes come together to fight an existential threat. I would have considered to put a bit more emphasis on a hero, or perhaps a group of ordinary people acting heroically, inside the bubble and cut off at the start of the first battle (i.e. putting the focus on the danger and figuring out the solution to the first big problem), but then I like cliff hangers perhaps a bit too much and I am certainly not the author to determine what would be better for the story.