The limiting factor inherent in neural nets is the relevance of the 'training set' to the actual circumstance.
Training a neural net is basically a matter of superimposing a new set of relationships and values on the base set or sets. This idea might be helpful if a certain type of fundamental failure - not already anticipated in the aircraft design & redundancy principles - could be 'trained' into the NN controls for future availability in the event of that or a very similar contingency. But there must be a fairly short list of such contingencies that are both flyable and not already accounted for. The trick of steering with engines-only is a good one...probably wouldn't be a bad choice to include it somewhere down the line in production aircraft, but then folks will have to periodically test it, and use it in sim training, and maintain it, etc...
The bottom line is that every new feature / function has an initial cost, a training cost, a support cost, etc. For things considered to be extremely low probability, the weight of trade-offs often countervails the putative benefit.
Neural nets are probably a good way to implement aircraft controls altogether. Accountability is a problem. They are, by definition, non-deterministic automata that don't always give the desired answer to the 'standard' set of constraints - just like people. Probably NN controls are a good intermediate step on the way to truly intelligent controls and systems. We can build those today that work pretty well. We just can't PROVE that they will always work when needed. Because they won't 'always' do any specific thing in the exact same way.... just like people....but it is much harder to look them in the eye to see if they can be trusted.