That's just wrong, we know this not to be the case from QM information theory and from thermodynamic arguments! This is the main point Hawking was making. While we don't yet have a good microscopic theory of what's going on, macroscopically we know that the information (entropy) doesn't just vanish into three numbers.
What information could one possibly extract from a "packet" of Hawking radiation? If the black hole was originally formed from a huge mass consisting of 80% iron and 20% xenon, for example, could such a thing be deduced by inspecting the radiation emitted by it? I would suspect that the answer would be "no". (Of course, I am just being an arm-chair physicist here.)
What does that even mean though? Certain systems may indeed time-reversible, but I would argue that most are not (practically speaking). Imagine for example a meteorite which has fallen to Earth. In order to "reverse the process", not only would it have to "reassemble itself" from the innumerable pieces embedded in the ground, it would also have to be flung back passed the escape velocity of our planet!
> But this seems to break down when it comes to black holes (it also breaks down in the various magical collapse interpretations of quantum mechanics, but the quantum wavefunction itself is also time-reversable)
I still don't understand the issue. Entropy is essentially just a measure of how close to a system is to the "average value". A high-entropy system being very close to it (and hence, "highly disordered"), while a low-entropy system might be two or three standard-deviations from the mean. A black hole with little angular momentum, charge, and/or mass would necessarily have a lower entropy than otherwise, but in any case we can calculate that without knowing a thing about what is going on inside of it. Moreover we can deduce that such a black hole would indeed be "easier to time-reverse" than one with a higher-entropy, but what does that even tell us? As far as I can tell, not a whole lot.
So the question is, could a pure quantum state model a meteor crashing into Earth? It doesn't seem like it. Friction, heat, and so on cannot be reversed classically. The question of Schrodinger's Cat even becomes moot because in an isolated system, the processes a body requires to sustain life (such as friction and heat) can't be modeled in the first place, so the cat will turn into a sloppy goop before anyone pulls the trigger. So, what's going on? Why does quantum mechanics seem to model everything that happens in the microscopic world, but in the macroscopic world we see things that it can't? Where does that crossover between microscopic and macroscopic occur? If measurement is what causes quantum wave collapse, then would none of this happen if nobody was there to measure it? And what created the measurers? 99 years since Schrodinger's equation, and we're not particularly any closer.
Black holes also seem to violate reversibility. They absorb information, but the radiation they give off is random. So, it's impossible to perform the process in reverse. This is spooky in a different way than the above because it's purely mathematical. For "regular" micro/macro quantum/classical paradoxes, we're generally talking about the classical realm of experiments. But for black holes, it's pure math, of our two fundamental theories of nature, and showing that they don't line up. Though, it's perhaps less spooky because the obvious answer is that one or both of the theories is slightly wrong, so we just need to fix it. The measurement problem, or understanding waveform collapse, I think is the more interesting problem, but that's just me.
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You're not contradicting my argument: I'm saying that there is only a "before", and never an "after". Saying that light emitted before crossing a horizon is visible in a finite time is not incompatible with what I'm saying.
Keep in mind that Hawking's model is known to be oversimplified as well! In his simple evaporation model, the information encoded in the infalling matter is lost, violating QM information conservation.
If you simply assume that no infalling matter ever crosses any horizon, that it all just "blows up" very slowly from the perspective of an outside observer, then there is no QM information paradox, no inconsistent observations, etc...
If you disagree, please cite a recent paper.
Here's a nice thought experiment for you: What happens at the last moment of an evaporating black hole's life? How does the horizon "disappear"? Whatever you imagine happens, now update your mental model for a relativistic observer. What do they see? I.e.: Does the increased apparent mass delay the observed disappearance of the horizon!? If so, how can this be? How can two observers disagree on the presence or absence of this horizon? Now consider what would occur at this juncture if there was only smooth curvature, no horizon, and no singularity. Would this enable the last moments of a BH's life to be consistently modelled for all observers?
Now, it's entirely possible that a complete theory of quantum gravity comes out and upends our understanding of what happens everywhere in space, including at event horizons, and perhaps it's the case that black holes are never formed. But to date, a fully consistent theory of quantum gravity has yet to be created. But just saying "assume black holes don't form, and all contradictions go away" by itself doesn't really help, because that just says get rid of GR and/or QFT, but doesn't say what to replace them with, beyond "something that doesn't produce black holes". Which, sure, would be great, but the devil is in the details. The more important thing to most people in the field is solving the UV divergence problem anyway, which will answer in detail questions about Planck level effects. Whatever comes out of that will (hopefully) unfold naturally into the answer to the information paradox too.
As far as the final question, nobody knows. That said, care is needed when describing events from different perspectives. The principle of relativity isn't that all observers agree on all events. It's that physics is the same in all frames of reference. Which is nuanced: what does one mean by "the physics"? In essence, it's a layman's statement of Noether's Theorem, relating symmetries and conservation laws. So, depending on quantum gravity's symmetries, different observers could see wildly different sequences of events, but they would agree that the conserved properties of the theory were indeed conserved. But until such a theory exists, it's anybody's guess as to what those symmetries actually are.
In the classical approach, the light that the object emits a second before crossing the horizon will take years to reach the observer, at a millisecond it'll take decades, at a microsecond it'll take centuries, etc. But it's always still coming, never stops completely. So in the classical analysis, an observer will always see the object, unboundedly redshifted, infinitely near the horizon, but not quite there, forever.
However, in the presence of Hawking radiation, the black hole loses mass, and thus the horizon shrinks. When this happens, that last bit of light the object emitted before crossing the horizon will now reach the observer in finite time. In particular, the observer will see that long _before_ they see the black hole evaporate entirely; one photon's worth of radiation is enough to do the trick.
You're correct that the object will experience this time dilation by seeing more radiation as it gets closer to the horizon. It'll also start getting pelted from behind by infalling radiation. But nothing will blow up as it crosses the horizon, so it'll safely continue on to experience whatever quantum-graviational phenomena happens at/near the "singlularity".