If we imagine aa is an accepting state, then we can imagine that a+ is a good return value. And it's easy. That doesn't mean it's a good idea since accepting aa may be a bug in our larger code.

Well, any heuristic like that is possibly going to give either false positives or false negatives when applied to a set larger than the training data. A pure white-list approach is definitely an option for determining the accepted inputs, but generally some heuristic that attempts to accept inputs "like" the examples will probably be better.