I'm butterfly fundamentalist in theory, but in practice it is hard to write TL, if every random event, including conception, MUST be different from OTL. I treat AH more like tought experiment.
Also, there is another problem-our knowledge of the past is limited, we don't know, what Mr. X was doing during periods of his life not mentioned in history books, we don't know about all interactions between person X and Y, more we go into details, we see more connections between event A and event B, even if they seem to be unrelated at first look, with unlimited historical knowledge we'll see even more. So any TL is by default only approximation, not exact simulation of possible, alternate path of history.