The team owns the code collectively, which means that no developer owns any component. This practice complements moving developers around to different areas of the system and the drawbacks to that practice also apply to this one as well.
What if 2, 3, or more developers each decide that a certain component really should be written in a different way. Who gets to decide how it should be done?
What often happens is that the component ends up with a potpourri of ideas and techniques. It can lack consistency of design which can make the component harder to understand and maintain.