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Why would that happen? In a different coordinate system (Kruskal–Szekeres coordinates) nothing special happens at the event horizon at all.

Why wouldn't it happen? From the perspective of anyone outside the black hole, nothing can ever enter it. What if that's just true?

Have you considered that the apparent event horizon is not uniform for all observers?

So does spacetime exist in some frames of reference but not others because those frames disagree on the radius of the apparent event horizon?

Also note that in general an event horizon doesn’t require a singularity.

All observers outside the black hole agree that nothing ever enters the black hole though.

And all observers on the event horizon agree that there is no event horizon :)

What I’m trying to say is that there is nothing special about the region of space near the event horizon.