It's kind of amazing really that the near future will probably be about removing massive amounts of code & design from all sorts of incredibly carefully engineered systems like the linux kernel in favor of a pile of linear algebra that can just figure things out. resistance is futile.
(Less flippantly - neural nets are mainly for the case where you can't effectively do manual feature engineering because your inputs are too varied and complex, you don't particularly care about the mathematical properties or guarantees of the solution, and where you don't even really know what the solution should look like [so are forced to randomly initialize a huge nonlinear system and optimize it until useful behaviors pop out]. Something like predicting path saturation would be far better suited to traditional approaches.)
Edit: By the way, I accepted your initial opinion about traditional approaches being better at face value but that was like ~45 minutes ago. After thinking about it a bit more I realized that there is alot of interesting network data that could be fed into such a NN, moving it (ding!) back into the nonlinear/complex system column. Suddenly my approach is looking competitive to also being the optimal one (excluding hybrids).
Care to elaborate?