I generally like Sabine’s work, but this isn’t even close to true. It’s unsolvable now, and maybe it always will be. But we’ve thought a lot of problems were unsolvable that we’ve since solved.
And she’s also not really right about information loss — time irreversiblity and information loss are the same thing. If a quantum process is time irreversible, then initial state information is gone forever. Is one a better phrase than the other? I don’t see why it matters much, though of course physicists prefer “time irreversibility” because that’s closer to how their equations are most commonly formatted (though it’s possible to format this in an information-theoretical way too, just not regularly done because it’s much harder and not taught that way).
I don’t understand why this is an issue. She takes Hawking radiation for granted, which has never been observed and very possibly never will be, but concludes that we cannot ever solve the time irreversibility problem of black holes? That doesn’t really make sense.