It is a good idea, and we could probably try it sometimes, however I need to poke a few holes in it to see if you can patch them up.
1. In FFA you spawn everywhere, even in the "other team's base." This could make it hard for a team to hold a certain position.
2. Everyone would show up as an enemy on radar. It will be impossible to tell an enemy from a friend. Also, since there are no team colors, you'll really have to know who is on your team because it might take a second to figure out if you should shoot or not.
3. It will take some quick adding to figure out who is ahead. Knowing who is winning usually effects how aggressive your strategy is.
4. We would have to restrict who could join the game. If a new person joined, not only might they think it was a standard FFA, but even if they thought we were doing a team thing, they wouldn't know what team to play on.
If we can work some of this out, we could give it a shot.
OR, find a hacker and have them turn on "Team Kills" in the debug menu. That feature does exist in the game, but it was deactivated and hidden. Lame right?