the fact that the filmmakers were trying to hard to push a premise that was just too full of holes.
I don't think that this movie is meant to be taken too literally. Battle Royale is another one of those movies that have something of a cult following, but for all the wrong reasons (the dark & edgy subject matter of high school students killing each other, the gore). I'll try to explain...
Does your copy by any chance feature the making of? If it does, first thing you notice is that the director Kinji Fukasaku is not at all the kind of guy you would expect directing a film like Battle Royale. He's basically a soft-spoken old geezer. So, why would a guy like that, who is mostly known for his yakuza films, be interested in bringing some bestselling novel about teens being forced to kill each other to the big screen? Here's the thing: During the latter stages of WW2 the director was about the same age the students portrayed in the film. There is a moment in the Making Of where he tells the young cast about his gruesome wartime experiences (something about having to remove his friends' body parts after an air raid on the factory they were ordered to work in). These experiences have instilled in him a strong anti-authoritarian streak, which also explains why he devoted most of his films to social outcasts, like his yakuza characters.
The film is essentially about Fukasaku exorcising his wartime trauma. The novel the movie is based on is set in an alternate history, where Japan won the second world war (something that's not explicitly said during the film), the same government that caused Fukasaku so much pain. It's easy see why this subject matter appealed to him.
Personally, I really appreaciate this film. It has a sincerity about it that you won't find in too many films these days.
Speaking of Fukasaku, everybody should check out his criminally underseen "Under the flag of the rising sun", which makes a nice companion piece to Battle Royale and is one of the absolute best anti-war films ever made.