> The theory is not wrong, but in practice it's often irrelevant. Sure, any algorithm you can come up with will blow up on some inputs. But you might get a fast solution on 99.9% of inputs.
A lot of simulation we only have exponential-time algorithms for. Motion planning, protein folding, etc. For a lot of these today, the SOTA is to use an NN model to learn the heuristics from data. OP's claim only rings true if one can only think of just the algorithms that undergrad CS now studies.
The neural network approach should be able to crush any NP-hard problem into an easy problem for the subset of real world examples, although not for all possible examples.
When you say "The neural network approach"... you are effectively refining the problem space into something smaller based on the data that you are training the NN on.
(Note: I'm speaking vaguley, on the same vague level as your comment. I can be more precise as to what my indications indicate)