Earlier quoted context omitted.
> it is just a mathematical artefact of weirdly chosen coordinates. No, that's not correct. The fact that the singularity is always in your future inside the horizon is an invariant, independent of any choice of coordinates. > the singularity is still just a point in space No, it's not. A point in space would be a timelike line in spacetime. But the singularity is a spacelike line in spacetime. That's a moment of tim…
Just draw the geometry in Eddington Finkelstein coordinates and you will see everything I wrote above is true at the technical level if you read precisely.
That also makes your use of the term "spatial coordinates" questionable, as I already pointed out. The fact that the line r = 0 is vertical in an Eddington-Finkelstein spacetime diagram does not mean it's automatically a "point in space" or that r inside the horizon is automatically a "spatial coordinate". You need to look at the actual physics, not just the surface appearance of the diagram.