What are, if they exists, any historical reason why there is not draw in the main US sports (NBA, NFL, NHL, MLB)?
I know that draw is possible in NFL, but this events is so rare that I think is it possible to consider it a sport with "no draw"
I don't think you'll find any explicit historical events or conditions that led to the absence of ties (mostly) in U.S. sports. I think it's just a product of the sports fans' sentiments that frown upon ties and draws. For most sports, it's not incredibly difficult to "untie" the game either. Since baseball is one of the most influential games in American sports history, I have a feeling that sentiment would be a little different if draws were used in the early days of play instead of extra innings.
The common perception in American is that ties are a waste of time and pointless. People like things black or white, good or bad, won or lost--ties are a shade of gray that's not very exciting, and excitement is one of the aims of sporting events. Each game is billed as a contest to determine the better team and American fans don't like inconclusive results. A lot of people see it this way--why play 2 or 3 hours to a tie when the result is basically the same as if the game was never played?
For places around the world where draws are common, there's probably a little more nuance in how to look at this. A tie could be seen as a good or bad thing depending on the teams and it's all part of a long season. But Americans are more likely to want to know right now and keep it simple: who won and who lost? "Neither" just isn't a satisfying reply.