There's many good answers to this on a physical level, but I don't see this one addressed, so I'll give an answer briefly.
I'm just having a hard time accepting that anything can exist with an
infinitely large property as it would lead to infinitely large mass
leading to infinitely large forces...that would just destroy the
universe infinitely fast, wouldn't it?
If black holes have infinities, which is only possible if they have a singularity, then those infinities are, by definition, infinity small and not infinite from any distance away, even a fraction of an atom's distance away. So "destroy the universe by infinite forces", sure, if the universe was smaller than an atom, or maybe, inside the event horizon where it couldn't do anything but fall towards the singularity, but at any safe and reasonable distance, black holes aren't dangerous and not a threat to the universe.
So I think a supermassive object can be a badass just as well without
having to be a singularity
Gravastars to the rescue! Just what I needed. Finally, some theorists
who are not comfortable with infinitely nasty objects populating our
OK for starters, the laws of physics are what they are, and they don't care what we think. As to things being "nasty", that's in the eye of the beholder.
2000 years ago, "hellfire" was magma seen coming out of the occasional volcano and hell was inside earth. Today, the inside of the Earth generates a magnetic field that protects us and gives us plate tectonics, which is really useful for life bearing planets. The inside of the Earth hasn't changed, but our perception of it has changed enormously. Now we love the inside of the Earth, but 2,000 years ago people feared it.
100 years ago, everyone thought the Universe was the Milky way and 80 years ago, they thought the Universe was eternal, until that lousy Hubble suggested the Universe had a beginning and, well, so much for things being eternal. If Hubble had said that 300 years earlier he'd have been burned at the stake, no question about it, with a plaque that stated "blasphemer"
That's the problem with point of view. It's not a complete picture. Black holes make a great "boogie man", as something that eats everything and cannot be escaped, but that's only part of the big picture.
Einstein himself found black holes a distasteful idea (He wasn't too keen on quantum mechanics either), so Einstein imagined the Universe had some physical law that prevented black holes from ever forming and that might even be the case, but honestly, how different is it to be slowly squashed around the event horizon over an eternity vs quickly squashed in the singularity or whatever goes on in the center. From a certain point of view, it's pretty much the same thing.
Some theories have gone so far as to suggest black holes are magical places with entire baby universes inside of them. I find that more creative thinking than science, but the truth is, what happens inside the event horizon stays inside the event horizon and nobody knows.
On black holes in general:
They're very useful. The formation of black holes, and the gravitational collapse and rebound off the collapse, creates and distributes heavy elements across the galaxy and in the collapse that creates a black hole or Neutron star, something like 90% of the matter of the star gets blown off, recycled, if you will, back into the galaxy and only 10% or so, forms the collapsed core.
You can think of the black hole as a nasty little remnant of a star's death, but I find the fact that large stars recycle and distribute so much of their matter across the galaxy to be highly cool. Supermassive black holes also help in the formation of galaxies, so the simple truth is, black holes are very useful, even if you wouldn't want to cross paths with one.
Now on what happens inside a black hole, there's some good answers to that already and I don't want to make this too long, especially since I'm a layman, but I find the speculation of that exotic region inside the event horizon to be great fun to think about.
I personally don't believe in singularities. I (THINK), that the wave and field nature of quantum mechanics and the fact that empty space has properties which, for example, particle anti particle pairs can form essentially out of nothing, (which make hawking radiation possible), I think there's probably some kind of exotic space of never a full singularity.
I don't think there's what might be called a physical material inside a black hole. I think things would behave differently than that, more like the exotic nature of a proton or electron than the physical nature of a surface, but that's just my thoughts on the subject. Without a quantum theory of gravity, it's a bit like the blind looking at a map though. Nobody knows. (too long?)