The NFL would require a huge increase of international viewers and advertising revenue to offset the significant loss of U.S. revenue. Since this isn't going to happen, there's no way owners will approve.
The Super Bowl TV audience would be much less if the game were played at 4:00 AM. Nobody is hosting a Super Bowl party at 4:00 AM. Casual fans and people who only watch football when it's the Super Bowl are viewing for the pregame entertainment, halftime show and commercials; they won't be waking up early to catch a game that really doesn't interest them. I suspect there would be a large number of people who, like me, wouldn't bother watching unless their favorite team were playing. Even at a less absurd 10:00 AM, there would be few people having parties. You'd also have a problem with bars and restaurants currently showing the game who are not open in the morning, do not serve breakfast, and who would make much less money on alcohol sales if the game took place so early in the day.