It's the same reason why you can't use pictures of people in public or their quotes or tweets for commercial reasons without permission: there's a general concept of human dignity and privacy that includes people's thoughts, words, and appearances/etc as belonging to them. It's not greedy to want respect for basic human autonomy.

Plus pragmatically speaking this sounds suspiciously like something that's "not a problem" until it is a problem. If a poorly written LLM regurgitates my name and lines from a blog post (or god forbid hallucinates a blog post by me as a citation) in some defense of Pol Pot or something that's going to be come a problem for me very quickly.

EDIT: Fridge thought: quite frankly if someone's making money off my interactions in this economy you can bet your last dollar I want my fair share of it. It's not greedy to gain value from your interactions with the world: you already do by interacting since that's a bi-lateral relationship ie it affects each party equally. It IS greedy for a third party who did not participate in the interaction to expect value from it.