You only get paid more when you can convince someone else that you should be paid for or that your boss is afraid of losing you. A super competent noob will still get paid just noob wages because they don't have leverage. Leverage comes with experience and time, which doesn't sound right but it just is because people have a hard time quantifying experience.
Also, companies will rarely see you as the value you contribute. Things might slow down when you leave, if you are actually that productive, but companies get bent on paying average wages even if it hurts them. Companies don't like employees ransoming them and paying above average sets a precident for other employees. You don't have as much leverage as you think you do because companies are dumb. The only time I have seen someone having a massive amount of leverage was in a small engineering firm with an experienced and very specialized engineer who could not be readily replaced and could command a very high wage from large companies. In that situation, the guy was basically made partner with the owners.