general relativity - Why do physicists trust black hole physics?

Based on popular accounts of modern physics and black holes (articles, video lectures), I have come to understand the following:

1. Black holes are predicted by General Relativity, a classical theory of gravity.


2. We know that the universe is inherently quantum mechanical, so we believe General Relativity to be somehow incomplete or inaccurate.


3. We do not have a quantum mechanical theory of gravity.


4. We know that (on some level) General Relativity and Quantum Mechanics are incompatible.


5. There is no direct experimental evidence of event horizons.

If all of these things are true (and if they aren't, please correct me), why do we trust black hole physics? How can we talk about something like Hawking Radiation if it uses both General Relativity and Quantum Mechanics and we know that we don't know exactly how to unify them.

When I read about or hear physicists talk about black hole related phenomena they speak with some considerable degree of certainty that these things actually exist and that they behave in the way the known physical laws describe them, so I'd like to understand why in the absence of direct evidence or a unified Quantum Mechanics/General Relativity framework we can be so confident in black hole physics.

EDIT: I just want to point out in response to some of the answers that I am aware of the evidence of very massive objects which are very compact and are believed to be black holes. I do not doubt that there exist very massive objects which have a great effect on the propagation of light and distort space and so on. When I talk about "black hole physics" I specifically mean physics which is derived by combining quantum mechanics and GR such as Hawking Radiation, things relating to the Information Paradox, etc. That's also why I specifically mentioned event horizons.

Answer

At first many people didn't care much for black holes. But later people showed that they were pretty unavoidable features of the theory of general relativity and that theory made other quite precise predictions that were tested and found good.

So when you are told that black holes are required if you have GR and GR looks like the best game in town then it becomes less bothersome.

But there is more. Having a detailed classical theory of black holes gives limits on the sizes of neutron stars, and we see neutrons stars. So you can look for neutron stars, look for evidence of their mass and now if you see one that is too large you can disprove GR. So people look. And GR wins again.

And eventually we start to see objects that behave like we expect a black hole to behave. So it makes sense to refer to things as black holes. Because they are enough like them that theories about black holes can work.

You still make a line between what has been observed and what hasn't. And Hawking radiation is on the wrong side. But if someone talks about Hawking radiation with certainty they are probably trying to explicate a known theory's predictions rather than an experimentally confirmed fact. But it is always important to distinguish between new results and known results, so the apparent certainty is probably an attempt to say "I am not saying something new" and it just comes off badly.