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Speaking as a programmer, neural networks will never be suitable for most purposes. For example, it is impossible to make a neural network which will give perfectly accurate results for simple integer addition or subtraction, merely one which calculates close approximations. However, for certain fields, such as image recognition, neural networks are the only way to do it well.

Edit: "This works, but might someday destroy the earth if some unknown and very specific parameters are reached." won't ever be a thing, because we can use maths to find whether certain outputs are possible. Neural networks merely take inputs and produce corresponding outputs once frozen.