What? Lighten up on the philosophy of a topic before you understand it.
Sure, the physical reality of the singularity is a bit of a mystery as it comes up against the nature of gravity at an extreme which requires a quantum theory which includes general relativity, but that is a known unknown and not what any of this black hole physics is about.
Outside of the singularity, and definitely outside the event horizon, a black hole is a very real thing which has been seen and measured in "empirical reality" and theory has so far matched well with measurement.
Nobody is going to Euclid and claiming a point or line is a real physical entity, anything but a useful abstraction.
Sure, the physical reality of the singularity is a bit of a mystery as it comes up against the nature of gravity at an extreme which requires a quantum theory which includes general relativity, but that is a known unknown and not what any of this black hole physics is about.
Outside of the singularity, and definitely outside the event horizon, a black hole is a very real thing which has been seen and measured in "empirical reality" and theory has so far matched well with measurement.
Nobody is going to Euclid and claiming a point or line is a real physical entity, anything but a useful abstraction.