Beverly Hills Cop wasn't nomianted for Best Picture. Neither was Top Gun. Or My Big Fat Greek Wedding. All tops in their year under your qualifications.
I agree completely. As other posters have noted the movie was a work of art. It was also riveting and intense and draws the viewer in. It also becomes nearly to real by using the actual spoken language of the time. Has any movie with subtitals ever won for best picture? This one should. If Alexander can be looked at as an historic figure in a movie why can't the hollywood elite get over their religious bias and just look at this as true history to be objective? They can't out of fear at looking at a masterpiece of cinema and giving credit because they are trying to kill the message of the movie itself and just like the pre movie hype which helped to spread its fame, so also their post movie ractions and snubbing will further work against them with even more of a negative impact on hollywood and gain more popular support for this film and all those that starred, directed, produced, and participated in this movie. Studios and production companies are born this way and the audience decides who stays in business with their dollars at the box office.