Uni-the-Unicorn!
Hero
I will clarify that I don’t like other mechanics that “push” the story. By push I mean actively advance the story. Leveling is passive, and, in our games, story dependent. We level when the story dictates, not the other way around.So you've never played Zero to Hero? And in your 20 years levelling up has never impacted the way characters behave or their place within the game world?
I'm afraid I simply do not believe you here. Levelling up is a textbook example of mechanics pushing story. You might find that the mechanics don't interfere with the gameplay that much because you accept what they are trying to do - but that doesn't make them not mechanics that push a story.