I think it’s too early to say what differential lambda calculus or linear logic is “good for” in a practical sense. However, I don’t tend to think of it as being about breaking problems into smaller pieces.

I think it is more about error propagation: you can’t estimate which inputs to an algorithm contribute more to the final error, without some notion of derivative of an algorithm with respect to its inputs (even if those inputs are discrete, so that making infinitesimal variations does not obviously make sense).