Well, objects falling into a black hole can reach the singularity in a finite amount of time. So you're going to have to enrich these singular spacetime points with a lot of extra structure if you want whatever passes through them to still exist. ¯\_(ツ)_/¯
To wit, you can imagine classical black holes as pulling whatever's near them into the future. The effect is so severe when you pass the event horizon that escaping the black hole amounts to traveling backwards in time. The effect is so severe when you reach the singularity that the entire timeline of the universe is in your past. So the singularity itself is more like an infinitely distant future than a point in space, with the caveat that the black hole slings you toward it with enough acceleration that you either actually reach it or something about this classical picture breaks down.
I feel like there's something so scary about falling into a black hole, literally unable to escape, that we just really, really want it to be "survivable", somehow.
Which is kind of funny when you consider that no one would expect to survive falling into a star, but we don't grasp at straws the same way to say, "Oh, you wouldn't actually be immolated, the solar wind would blow you back into space first."
To wit, you can imagine classical black holes as pulling whatever's near them into the future. The effect is so severe when you pass the event horizon that escaping the black hole amounts to traveling backwards in time. The effect is so severe when you reach the singularity that the entire timeline of the universe is in your past. So the singularity itself is more like an infinitely distant future than a point in space, with the caveat that the black hole slings you toward it with enough acceleration that you either actually reach it or something about this classical picture breaks down.