I get your point, neural networks could be some kind of black boxes and how the sequence of operations evolves might not be so dependent on the accuracy of each

I get your point, neural networks could be some kind of black boxes and how the sequence of operations evolves might not be so dependent on the accuracy of each operations -- at least, it would be a good intuition to believe "accuracy at each step matters" but it's not rigorously proven ? We could empirically check this by training a neural net and adding some random noise at each step