I mean, the three sisters works wonderfully as long as you're not trying to harvest mechanically or minmax your yields. It's a great way to produce food for a family or small village with a comparatively small amount of land and effort.

It's common in backyard and community gardens for a reason. To my understanding: (1) corn is a fast growing, relatively high yield calorie and carbohydrate source and provides a natural trellis for (2) beans which stabilize the stalks and provide a protein and vitamin source, while (3) squash serves as a ground cover to retain moisture, limit weed growth, and produces fruit high in fiber and vitamin C.

The beans do fix nitrogen but this only plays a role in replanting for the next season, reducing or eliminating the need to fallow.