Well here's an argument for interpretability: how do you know when your model will fail?

One tradeoff might be that with deep learning, it's unlikely to fail, but you won't know when it will. With conventional methods, you may not get as good of a performance in comparison, but have a better sense of the domain of applicability because you have a better understanding of the feature space (for instance, you can determine similarity of new data in this feature space when it arrives to determine whether it is similar to past data your model has been trained on).