I believe you are right, and that the Childs paper actually beautifully quantifies your suspicion: they appear to show that the speedup of the quantum algorithm

I believe you are right, and that the Childs paper actually beautifully quantifies your suspicion: they appear to show that the speedup of the quantum algorithm disappears if 'R > sqrt(2)', which intuitively means that the problem is 'too' non-linear. (I would expect that truly chaotic systems fall into this category.) This negative result does not seem to be mentioned in the quanta article.