Then you are misunderstanding her position. She is not claiming that a convincing solution to the BHILP is impossible. If you came up with a theory of quantum gravity that can be measured in other regimes and that also solves the BHILP, perfect: we now have good reasons to believe that your theory is indeed THE solution to that problem.
However, if you come up with a theory that makes the exact same predictions as QM and GR except for the BHILP, then your theory is not very interesting, since we will never be able to test this theory, and there are other inconsistencies between QM and GR that you haven't solved, so we can't just rest on our laurels and say physics is over.
I don't think I misunderstand her position. She seems to take the position you give:
"However, if you come up with a theory that makes the exact same predictions as QM and GR except for the BHILP, then your theory is not very interesting, since we will never be able to test this theory, and there are other inconsistencies between QM and GR that you haven't solved, so we can't just rest on our laurels and say physics is over."
I think this is wrong. There are non-empirical reason reasons we might prefer the new theory to the old one. For example, we know QM are GR are inconsistent, so if I give you a parsimonious, consistent theory that captures both QM and GR in the appropriate limits, then that's a great reason to prefer it. In principle, we could prove theorems (and some theorems of this form have been proved) that pin down the possible resolutions of the GR/QM inconsistency. If we tighten the net so that only one theory remains, then obviously we should choose to believe that theory.
Now, will that actually happen? I don't know. But merely waving your hands and going "not testable" is not enough, because we all accept that mathematical consistency ought to have a huge influence on theory choice. You need to make some argument about BHILP specifically saying that theoretical arguments will never produce productive physics.
> For example, we know QM are GR are inconsistent, so if I give you a parsimonious, consistent theory that captures both QM and GR in the appropriate limits, then that's a great reason to prefer it.
Absolutely agree. But BHILP is not the only inconsistency, so if you only solve that one and leave the others, but complicate the math or add other elements that can't be tested, it's not a particularly compelling theory.
So, why not work directly on the other inconsistencies, which might be directly testable, and see if this one disappears that way?
To be clear, when I say other inconsistencies, I am referring to things like making QFTs work in a non-flat spacetime, and/or reconciling the linearity of QM (without Born's rule) and the non-linearity of GR.
> So, why not work directly on the other inconsistencies, which might be directly testable, and see if this one disappears that way?
These are not mutually exclusive options. The community works on both.
Again, I agree that so far, practically speaking, work on BHILP has not been super compelling. I take issue with the stronger stance that Hossenfelder seems to take, that we know a priori that work on BHILP will be worthless because experimental data is not forthcoming. ("And that’s why I stopped working on the black hole information loss paradox. Not because it’s unsolvable. But because you can’t solve this problem with mathematics alone, and experiments are not possible, not now and probably not in the next 10000 years.")
However, if you come up with a theory that makes the exact same predictions as QM and GR except for the BHILP, then your theory is not very interesting, since we will never be able to test this theory, and there are other inconsistencies between QM and GR that you haven't solved, so we can't just rest on our laurels and say physics is over.