You are correct. Even tree species in the legume family will fix nitrogen perennially instead of tilling in as a cover crop like clover or rotating like soy beans. I personally like to feed the biology of the soil, the microcosm of life is really what makes nutrients available for plants. So increasing organic matter for worms and fungus and bacteria etc, you're indirectly giving the plants easier food to use as fuel.

I do believe having one field completely filled with clover in a crop rotation system used to be standard in the old days.