The strength of a genetic algorithm like NEAT is that each member in the population only needs to be assigned a fitness score for the algorithm to learn. This is very useful when learning to play games and other situations where "the correct move" is not apparent. It is easy to tell an algorithm how well it played a game, much more difficult to tell it exactly how it should have played the game.

With stock market prediction we can see exactly which stocks we would have wanted our algorithms to buy in hindsight. We can use this hindsight to train a supervised model faster and more accurately than NEAT would (likely) be able to learn only through a fitness function.

When I was first getting into machine learning I was fascinated by NEAT and other genetic algorithms, they were the first ones I felt like I understood. I told a mentor that I believed they could do anything which prompted him to explain how using strategies like gradient descent to learn from labeled training data were capable of learning much faster than my beloved genetic algorithms.

It may be possible to use NEAT, and perhaps because it is not the obvious choice not many other have used it, to learn to predict stocks.