I think that most writers have an entirely different world in their heads (at least I hope I'm not alone in this). All day long I have characters who exist in my mind and nowhere else because I haven't found their story yet. And I have story ideas that go nowhere because I don't know where they're meant to go. They're scenes or sentences or characteristics, but nothing more. Because everything, and everyone, is fodder for my imagination.
Maybe the question, for me, isn't really why I write, but why I can't help but experience everything as an input. And by that I mean that people I observe or encounter, and things I hear and see, places I go are all inputs, like raw materials going into an assembly line - and that assembly line is my imagination.
If my imagination is an assembly line, and life's experiences are the raw materials, then what's the output? And what happens along that assembly line?
Well, sometimes the assembly line spits out the rejected materials part way through the process because something isn't right - characters aren't working, an idea just sucks, or something I thought would be great just doesn't come together. But when it does all come together, the end of that assembly line is a story. And a book.
Fortunately, for a writer, the raw material is endless (and free!). And maybe that's why the assembly line can take so long to filter through the all the raw material until something good results as the output.
So, why do I write? Because as long as there are raw materials, the assembly line doesn't stop.