The offside rule is one of the most difficult to understand because of the human error element by the referee or his henchmen.

Why not eliminate the offside  once the ball has passed the 18 yard line?

To simplify, between centre and the 18, offside is in effect. Once the ball passes by the 18, there is no offside.

For example: 

1.  On your side of the field, you kick the ball to your centre who is behind the defense past the centre line in the opposition territory--offside.

 2. You are in the opposition territory 30 yards out and you kick the ball to your centre who is behind the defense past the 18--offside.

3.  You scoot down the wing past the 18 and cross to your centre on the goalline--no offside.