> There certainly are massive objects at the center of most galaxies, and the most economical explanation is that they're black holes

That is just not true. To be a black hole it must first be possible for black holes to exist, otherwise they are simply supermassive object - to us they would look EXACTLY the same!

A black hole is NOT the simplest explanation! It's the most complicated one. You are using your razor very incorrectly.

> That they exist is beyond question.

Absolutely not true. That massive objects exist? Sure. Are they black holes? Not so clear.

> That they have super-high masses confined to a small space is beyond question. General Relativity then fills in the blanks in our observations.

No, actually General Relativity does NOT fill in the blanks - it claims things are impossible. The math does the equivalent of divide by zero.

> So is General Relativity. [a mathematical abstraction]

Great, so since GR predicts it would take infinite time, I guess case closed. Since infinite time, by definition, can not actually happen, it means black holes can not form. Just because you can calculate what something will do doesn't mean it will actually do it.

> Well, yes, they do -- they're giving up a huge amount of gravitational potential energy, and that energy must be conserved -- it's converted to kinetic energy, it becomes heat and light.

Kinetic energy does not become heat and light. Kinetic energy is velocity. To make heat and light you need some other process. Have you never heard of conservation of momentum?

On top of that, the discs are dim because time is dilated to nothing not because there is no energy there.

> But as matter falls into a black hole, in order for it to pass through the event horizon, it must give up most of its energy (both potential and kinetic). .... in that case, there would still be a huge energy conversion process .... Most of that energy is converted into heat and light.

How in the world are you writing this stuff? You can't just "give up" velocity. You have to transfer that velocity to something else. You can't just wave your hands and say "magic". Friction might cause objects to equalize in velocity, but can not actually reduce velocity (only share it amongst the objects).

> a black hole approaches its final form as mass approaches it from the perspective of a distant observer.

And takes infinite time to do so, and since right now is not infinitely in the future, right now, today, black holes do not exist.

Infinite. Do you not understand that word? It means forever, it means it never actually does it, just gets closer and closer.

> therefore if m1 and m2 occupy the same point in space, the result is infinite, therefore (because infinity isn't a number) Newtonian gravitation is bunk.

Nice question, wrong conclusion. The actual conclusion is that since infinity is not actually seen in the real world (as opposed to math), there must be some method that prevents the two masses from ever occupying the same spot.

Your argument is entirely backward, you think that if infinity shows up in the math then it must show up in the real world. No. If infinity shows up in the math then your math is wrong, or incomplete. In this case there is something else that prevents r from hitting zero.

Maybe you should read this: https://en.wikipedia.org/wiki/Domain_of_a_function