I agree that it is interesting as a thought experiment, and therefore as a fictional premise. But alternate history based on X not having existed is different from "everything as it was, just minus X." (This may actually be what you just said and I am not quite understanding) So, e.g. Europe between the world wars, by the way Rome never was (but all that did was to change the names of the places to eliminate the Latinity), doesn't make sense to me, and I honestly don't think that anyone would try to write it.

I also think that people wouldn't casually write out Greece or Rome (or the British Empire, or Charlemagne, or...) without thinking about the consequences because there is a certain amount of cultural affection: if you want the world to be basically the same, but with mammoths, you wouldn't want to lose them. And it's a bit saddening that there isn't that same affection for having indigenous American civilizations.