Perhaps fuzzy logic is like naive Bayes: When you don't have enough data to train a DL model or to compute joint probabilities with little error, you have to use simple tools with less power. Fuzzy logic is a system of simple (thumb rules) that in some cases can provide good results.

If, in a concrete case, fuzzy logic can provide you with some insight about a system then it is a useful tool for that case. For example, it is a tool for exploration about new hypothesis in case of having few data about a complex system. But when a lot of data is available then statistical methods perform better.

So I suppose fuzzy logic is a tool to use when having few data about a complex system, nothing more and nothing less.