I am a firm believer that design methodology can be applied to create solutions to complex problems, including those outside of producing a product.
I certainly think it is a superior methodology to the scientific method as it isn’t necessary to test one variable at a time that is the heart of the scientific method. It is extremely difficult to quantify complex problems/issues as stated in the OP. A design approach or a qualitative approach can look at the problem as a whole and is more likely, I think, to succeed with potential solutions.