I think scrapping the offside rule would not make the game more exciting, as some posted above it would only lead to long balls for the whole game.
I think if the offside rule didn't apply once the ball had passed the 18 yard line of the box, that it would be make it more exciting than abolishing it altogether. Strikers couldn't lurk around the box because waiting for balls to be lumped up to them, because they would be offside, as they would now. Once the ball reaches the 18 yard line (they could extend the line of the box to the sidelines, not the whole box, just the line so you know exactly when the ball is inside the 18 yard line) then players can run behind defenders. This would make it harder to defend and lead to more goals.
I wouldn't work like Ice hockey, you can be inside the area before the ball goes, as long as your not offside. Once the ball is played from within the area you can be in an offside position without being penalised.
For me this would add the element of excitement they are looking for, without turning the game into a long ball game.