The No Free Lunch (NFL) theorems state that no single optimization algorithm is ideally suited for all objective functions and, conversely, that no single objective function is ideally suited for all optimization algorithms. We examine the influence of the NFL theorems on a statistical experimental design (SED) application by exploring several design objective functions and several optimization algorithms for designing optimal azimuthal surveys to constrain a model of azimuthal anisotropy. Surprisingly, it is shown that the quality of optimally designed surveys is generally independent of the criterion-algorithm pairing (though it does depend on the optimization algorithms themselves). We demonstrate the principle of diminishing returns in SED, namely that the value of optimizing designs decreases geometrically with survey size. This implies that SED is most effective for the design of compact, information-dense surveys.