This does seem like a challenging problem to address, and as the authors mention, it also affects iterated amplification. (Intuitively, if during iterated amplification the decomposition chosen happens to be one that ends up being obfuscated, then iterated amplification will get to the wrong answer.) I’m not really sure whether I expect this to be a problem in practice—it feels like it could be, but it also feels like we should be able to address it using whatever techniques we use for robustness. But I generally feel very confused about this interaction and want to see more work on it.
Added an opinion:
I’d be interested to hear more detail of your thoughts on how we might use robustness techniques!