A few issues with that:
1. Cherry Picking: How are you going to reasonably stop someone from running around and killing people who's shields are gone?
2. Screen Peeking: How would we have a FFA with more than four people and prevent someone from looking at the screen-box directly to the left/right/top/bottom of theirs?
3. Grenades: Grenades are a very powerful tool when used correctly in any setting (tossing a brute sticky on the wall as you run by to catch the person chasing you comes to mind).
4. Weapon Choice: The Battle Rifle isn't good for every situation. Granted, it is a powerful weapon (even if you just spray-n-pray), just not as useful at extreme close range as something like the Brute Shot.
5. Time and score: Twenty minutes is a long time for a tournament match to run in a game like Halo. In 1v1 you can rack up ten kills in under five minutes with ease. Couple that with no score limit and you are liable to end up with one person having an unsurpassable score half way through the match, causing a lot of people to just put down their controllers and leave. There is also no way to end a match early when a clear skill difference has been established between one player and the rest.
Some questions:
What tournament style would you use (single-elimination, round-robin, etc.)?
What map(s) would people play on?
How many people would advance per match?
How would you break a tie?
Would you allow vehicles?
What power-ups (over-shield, active-camouflage) would be present?
Would you allow unofficial "teaming"? If not, How would you stop it?
Moral of the story: just because something is fun doesn't mean it is going to be a good tournament.
