Alright, time to really nerd up this discussion: theories of the Lady of Pain. What is she, exactly? I'm guessing she's and Overgod, comparable to Lord Ao. This would make Sigil something completely apart from the Forgotten Realms, as Lord Ao would not have any influence over Sigil. Instead of being a pocket plane, Sigil would be like some sort of "pocket Multiverse".
What came first? Sigil or the Lady?
I think your comparison to Ao could be in the right neighborhood. This makes me think of something that has come up from time to time in Alan Watts' lectures.
Here's an example. However, this is incomplete. This often gets coupled with the idea of metaphysical relativity. The eye cannot see itself, a tooth cannot bite itself, a mind cannot think itself. Putting it together, we are beings who exist interdependently and our existence is an activity, not a stable state of being.
On top of that, Sigil is a rather metaphysically sensitive place. Isn't there a part of the narrative where gods only exist if people believe in them? Perhaps Sigil itself only exists if a force believes in it. It's not really part of any of the other planes, but more in it's own space in between the planes (hence the idea that it may be the center of everything). Perhaps that is what the Lady is. She is a metaphysical force that exists to believe in Sigil. She is not a goddess herself, as then she would need worshipers to exist. If anything, Sigil is the god-being and the Lady is the faith-source that supports its existence. It would definitely explain how she can shape the city by thought alone. The Lady is Sigil's only faith-source (or at least has a majority share of it, since its residents can potentially make small changes to things), so Sigil becomes an extension of whatever she believes.
This could be why she doesn't accept followers, and to worship her has disastrous results. Were she to take the role of a deity, she would then need to conform to the rules of existence for gods. However, this would break (or at least be very damaging) to the Sigil-Lady synergy.
So, as Sigil is not a place that is a part of other places and doesn't play by the rules of other places, The Lady is a being that is not connected to other beings and doesn't play by the rules of any other beings.
My question is, why the Lady of
Pain. Pain seems to just be an incidental consequence of foolishly trying to worship her. If the core of her existence is this metathought cycle between her and Sigil, wouldn't that be the foundation of her name? The Lady of Dreams? The Thoughtweaver? Something like that?