The point I’m trying to make is that there are many ways you can be influential (including towards people that matter) and only some of them increase prestige. People can talk about your ideas without ever mentioning or knowing your name, you can be a polarising figure who a lot of influential people like but who it’s taboo to mention, and so on.
I also do think you originally meant (or conveyed) a broader meaning of influential—as you mention economic output and the dustbins of history, which I would consider to be about broad influence.
The point I’m trying to make is that there are many ways you can be influential (including towards people that matter) and only some of them increase prestige. People can talk about your ideas without ever mentioning or knowing your name, you can be a polarising figure who a lot of influential people like but who it’s taboo to mention, and so on.
I also do think you originally meant (or conveyed) a broader meaning of influential—as you mention economic output and the dustbins of history, which I would consider to be about broad influence.