Because you (or they or whoever ... I know you won't) will be paid to reveal it - either by getting more free stuff (like all consumer apps work today) or directly in a mechanical turk fashion. ie LLM providers will play the role of advertisers in the new economy - subsidizing everything in exchange for learning more about you, both to manipulate you and inform other endeavors.

Either way, when these LLM providers have consumed all existing information, the next frontier will be producing their own live and novel primary sources by manufacturing and distributing physical sensors throughout the world, and all we have to offer LLM providers then are our unrevealed preferences (which we will do because we will believe they are enriching us along the way).

Anyway, I'm pulling on this thread as a thought exercise primarily. I can imagine several interrupts or flaws in this. I'd still bet, like Gigi, that there will be refuge, but it smells like Pascal's Wager to me; ie if this is the end of everything I like, then I might as well keep doing what I like, just in case there's room for it.