It may look OK when new, but after having travelled a dozen times in your backpack it decomposes in the worst way. Pages start making a creaky sound when turning, they get stuck in the uneven wires, and inevitably start to separate, often from the middle of the page, which is extremely annoying and difficult to fix. When you try to re-fold the wires correctly with your fingers, it becomes worse. The only advantage with respect to spiral winding is that the actual binding act is faster to perform (but it requires a heavy equipment).

Spiral binding, on the other hand, is extremely elegant. It is the most robust shape ever, no matter how you compress it between hardcover books it always performs its job. The only way to separate the pages is by tearing the paper. You can bind them yourself with a simple multi-hole punch, and I actually find it a pleasing thing to do.

By the way, I don't understand your first comment. Spiral bound paper always lies open flat directly. On the other hand, for wire binding it may not (because the papers reach the fold of the wire).