I think there's an important meeting piece in your model- specifically, it's not a "progression system" that is necessary, it's progression, period. In Mario, the first level and the last level are different, and the last level is going to be harder, and expect you to understand more complex mechanics or level elements. This concept starts all the way back at Space Invaders, where the ships got faster the more you destroyed.
In a platformer, your progression is "new levels" and "new elements to the level." In a puzzle game, you might gradually introduce new mechanics or patterns for the player to learn.
In a typical RPG, the progression is new abilities to use and new enemies with their own new abilities to use against you. If this is done poorly, you fight the same thing over and over, but more 0s after every number. If this is done well, the game experience becomes more complex as you progress.