Oftentimes I see people encouraged to do orthogonal designs "so they can have a unique partition of the sums of squares" but I don't have any intuition on why that should matter or how it relates to interpretability. I'm thinking here particularly, but not exclusively, about the context of a One-Way ANOVA. Orthogonal designs produce balanced covariate distributions. It can be impractical, costly, and time consuming to set up an orthogonal.
Is there necessarily a loss of efficiency or interpretability if the experiment is unbalanced? If so, to what extent is this observed?
Some aspects of this question were explored, albeit in a rather shorthand way, in the answers to this question.