Yes. Or 7 a side. Played in the summer. Keeping players fit playing for their normal teams. Superstars only. Would make a shed load of money.
The problem with playing a rugby sevens style version of football is that it doesn't work well with the forward pass. I have a feeling that extra space would just promote long balling it up the pitch, rather the promote the running and athleticism we see in sevens.
You could add some sort of line system, making it illegal to pass the ball more than a certain number of meters, or across a certain number of zones (kind of like in ice hockey, where it's illegal to simply hoof the puck out of your end into the other teams (called 'icing') with some exceptions that make it work.
As others have mentioned, Gaelic football is awesome to watch, or Australian rules if you like your sports to be violent and insane.