The Roof Is the Whole Requirement

A sukkah is defined by its covering. The walls may be almost anything, canvas, board, an existing wall of a house, a hedge, and there are detailed rules about how many are needed and how complete they must be, but the sechach on top is where the halakhic weight sits. It must be material that grew from the ground and has been cut, so branches, reeds, bamboo or unprocessed boards qualify while a fitted roof does not. It must not be a manufactured vessel, and it must not be attached in a way that makes it a permanent structure. It must be thick enough that the shade inside exceeds the sunlight, and thin enough that the larger stars can be seen through it and rain comes through.

Joseph Karo's Shulchan Aruch works through these conditions in detail, along with the question of what invalidates a sukkah built under a tree or a balcony. The effect of the rules taken together is a structure that is unmistakably a shelter and unmistakably inadequate as one, and that is the intended result rather than a compromise between competing requirements. A roof that keeps out the rain would be a better roof and a worse sukkah. The rules about the stars and the rain are what stop the booth from quietly becoming a garden room, which is the direction convenience would take it in every generation.