The biggest advantage of a DOE analysis is that it provides a solution, and information about the space around that solution. This can lead to the engineer improving the design of the part, or changing an input parameter to improve the quality of the part.
Time to solution
A DOE analysis requires less manual input from engineers. Setting up a DOE analysis with current software is time consuming. Die trials can typically be shortened, as you will typically know which inputs affect part quality, and which do not.
DOE analyses can lead to solutions an engineer may not have thought of, and may help identify search directions that could improve part quality.
Scientific approach to provide better part quality
DOE analyses are robust, and have been used for a long time in engineering. Engineers typically have training in DOE, and understand the limitations. DOE analyses are an approved engineering tool. Therefore, there should be little resistance to the implementation of such tools.
Helps expand knowledge
By being able to relate physical inputs to physical outputs, in a real-time intuitive way, you are undergoing a self-learning process.