The quick story is that I don’t think the alternative histories within alternative histories are completely arbitrary. It seems to me that there’s a common theme in the best alternative history stories, a recognition that our world is the true one and that the people in the stories are living in a fake world. This is related to the idea that the real world is overdetermined, so these alternatives can’t ultimately make sense. From that perspective, characters living within an alternative history are always at risk of realizing that their world is not real, and the alternative histories they themselves construct can be ways of channeling that recognition.
I was also thinking about this again the other day when rereading T. J. Shippey’s excellent The Road to Middle Earth. Tolkien put in a huge amount of effort into rationalizing his world, not just in its own context (internal consistency) but also making it fit into our world. It seems that he felt that a completely invented world would not ultimately make sense; it was necessary for his world to be reconstructed, or discovered, and for that it had to be real.