This is field dependent, it feels more like an attribute of certain types of data rather than certain algorithms.
Reinforcement learning was on my mind when I was writing about "practical supervised learning applications" because yes, RL is different in that regard. And various function calculation examples (starting with XOR) indeed do so.
However, if we're applying neural networks for the (wide and practically important!) class of "pattern recognition" tasks like processing image or language data, then it's different, and those are full fields where you can easily spend a whole career working on just one of these types of data. Perhaps there's a relation with the structure and redundancy inherent in data like this.
I'm not even sure that it's not a problem in general. I know I've watched NNs frequently get stuck in local minima even on incredibly simple datasets like xor or spirals. SGD and dropout are widely used in part because they add noise to the gradients that can help break out of local optima. But that's not a perfect method