We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
No, I think that was Genghis Khan or Stalin. What Alexander the Great did was incredible considering his age and what he had to work with. Not saying it was peaceful or that he didn't wage war but just that it was an incredible accomplishment.
English and the languages that influence it tend to lump things like "formidable" and "large" (not just "very good") into the "great" category. Therefore, especially considering that it's an old phrase (like "Great Britain" and "The Great Fire of London", which don't AFAIK mean "Very Very Good Britain" and "The Very Very Good Fire" resp.), it could be (and I suspect it is) at least as much due to that ambiguity as it is due to any romantic whitewashing or glorifying his remarkable conquests.
I think Great in the context of Britain isn't very old, 1700 or so. I assume it's synonymous with Greater, as in the entire island.
Alexander the Great is a title just to distinguish him from other Alexanders. What was accomplished under his leadership was considerably above average, which fits the definition of several dictionaries. Great doesn't necessarily mean good.