My short answer is "Hell no!" I know that flicks like Hostel have taken gore to a whole new level, but gore is not the real aspect of this bloody cult film that people here in the US of A critics will boo-hoo over. It's the kids.
I own a copy of Battle Royale (and its so-so sequel) and it is a story of an alternate future where schoolchildren are pitted into battle against their own classmates. Their teacher is the head of the soldiers who drop these students on an island to kill or be killed. If they refuse, they die. If they try to run away, their heads will be blown off by an explosive collar.
I think it's pretty clear by now that interest group after intrest group would be outraged by an American remake of Battle Royale – and not because it'll most likely suck. New Line Cinema has not snagged the rights to Battle Royale – yet – but I bet that they could. When and if they do, there will be a lot of unhappy people talking about bad examples for children and child endangerment. Does anyone remember a director named Larry Clark? If people hate his work with a passion, why would they let a Battle Royale pass? The following is a quote from a New York Times article about Battle Royale:
Despite its success, the film was never released in the United States, and many in the industry said they thought it never would be. In post-Columbine America, they said, audiences weren't ready to watch 14-year-olds — even cute ones in stylish school uniforms — maiming and killing one another with axes, crossbows and automatic weapons.
I personally hope that no American film company gets the rights to Battle Royale, not because I am against violence involving children; I hope that they don't remake it because Takeshi Kitano and crew (including Kill Bill's Chiaki Kuriyama as a young girl) did such a great job originally.
If you really want an American Battle Royale, it's already here. Just go to one of the larger comic book stores in your area and the original manga is likely to be there. Better yet, Google it and find someone who will sell you a copy of the movie.