graph function singularities exist as physical features in our world
Do they, though..?
As I (mis?)understand it, as a massive star begins to collapse, getting denser and denser, the gravitational gradient gets steeper and steeper... and time (from the perspective of an outside observer) gets slower and slower... to the point that, from our point of view, the full collapse (or maybe even any collapse below the Schwarzschild radius?) hasn't happened yet, and won't happen until the extremely distant future, beyond the end of the universe...
So, in that sense, from the point of view of "our world", no singularities (except possibly the big bang) would ever exist (yet), all of them being censored not only by event horizons, but by being shoved into the perpetually far future, beyond time itself...
And, speaking about event horizons, isn't the whole "light isn't fast enough to escape" concept a misinterpretation of sorts..? As I (again mis?)understand it, it's not a matter of speed, but of geometry... The way space-time is twisted in such a gravitational gradient, once you get past the event horizon there are no longer any directions pointing towards the outside.
Which is another from of cosmic censorship (or a different effect or interpretation of the above), preventing anything inside the event horizon from causally interacting with the outside universe...
So, if these singularities are hidden beyond sight, causally, visually, and geometrically isolated from the rest of the universe, and perpetually shoved into the far future... can they really be said to exist in our world..?
(Of course there's always the big bang, but we can't really observe that one, only its effects, and it's not necessarily exactly what the original post was talking about anyway...)