Bras are structured to keep breasts from moving around. They are supposed to prevent sagging and strain on the neck and back. The purpose of the cups is to hold the breasts; the underband then holds the bra in place. The straps help to mete out the weight around the shoulders and upper back area.
Bra structure is important to understand because you should know how your bra works and how it should fit on your body. The straps should not be crucial to the support of the bra. They do help to mete out the weight around the shoulders and upper back area.