It is often presented this way because models generally mix up the observable universe and the universe. One key notion is that we are at the center of the universe. Not the Milky Way, not the Sun, Earth is. Yet we know that Earth isn't at the center, so what is that? Because it is defined as our ability to travel from where we are at. Each of us could be considered at the center of our own observable universes, but this is a distinction we don't make because they overlap so closely that we don't have tools with the precision to tell them apart. I would guess that even aliens on the other side of Milky Way have an observable universe that overlaps so closely with our that they are equal to whatever level of precisions our tools allow for. Once you get to someone in a different galaxy, especially one that is moving away from us and not closer, then they have a different observable universe.

But then, what is the universe? One way to think of it is to imagine that every galaxy has at least one intelligent species with their own observable universe. The universe is the sum of all observable universes. The very nature of how to sum them together, what it means to combine multiple sets of thing which include items that don't exist relative to other items in the set, is a question we can't really answer yet. Because of this, even a question like the size of the universe is unknown, and even the question of if more of the universe exists outside of the observable universe isn't simple to answer and gets into the nature of what it means to exist. If someone exists in the universe, but not in the observable universe, it becomes an instance of Russell's Teapot.