It needs to be open enough to see the stars. But if it rains we're exempt from dwelling in the sukkah. We go back inside under our year-round roof.
If so, why not just sit directly under the stars? Why is the pretext of a roof better than no roof?
Here's my take. A roof is the sense of self we have with which to build a nice life and take responsibility for ourselves and others. G-d expects to do and act in life.
On the other hand, the whole endeavor doesn't go if we don't see the heavens from within our responsible ambitions. The non-functioning nature of our roof is by design and command. It's a holy thing to work at making a roof. It's even holier when it's permeable to the heavens.