Black Holes are consistent with the Theory of General Relativity and observations of the Universe. Without them many phenomena would not be explicable.
When confronted with the extremes of science many people cannot come to terms with concepts so different from their everyday experience. Even some scientist cannot make the leap.
I recall scientists who showed that a bumble bee could not fly and a dolphin did not have the strength to swim so fast. Like in these cases, when we find an object that behaves exactly like a Black Hole despite their implausibility we must question the hypothesis.
There are theoretical questions about the plausibility of a Singularity, an infinitely small (well almost) versus the Event Horizon which is somewhat larger. It has also been considered that the Black Hole is actually the size of the Event Horizon.
However what lays beyond the Event Horizon is academic to a large extent since time stops and all matter and radiation is absorbed back into the fabric of SpaceTime itself. If you want to see a genuine "edge" of the Universe these Event Horizons are exactly that.