If you want to prove a result (for example the existence of a unique minimum-variance estimator) for a class of models, but can only prove it by restricting the

If you want to prove a result (for example the existence of a unique minimum-variance estimator) for a class of models, but can only prove it by restricting the class, then restricting the class is useful for that purpose. It may not be useful in applications, other than if you want assurances provided by results that have been proven about the class of model you're using.