Here is an example from mass spectrometry. Finding peaks in a 2D dataset.
https://pubs.acs.org/doi/10.1021/acs.analchem.9b04811
I think a NN approach is useful when you are interested in a certain kind of peaks. Like in this example, the author is interested in peaks with certain properties and other peaks are classified as noise. The NN provides a mechanism to learn arbitrary features of valid peaks only from provided (labeled) examples.