LLMs don't, but agents can easily be built that do.

An agent is not "just an LLM in for loop" (for what? Loop over what? Sorry, but such statements are hopelessly simplistic and devoid of careful thought.) -- agents perform actions.

One possible design of an agent would be to prompt an LLM to suggest a goal that would make the world a better place, then run an LLM in a loop proposing actions to implement that goal, executing those actions, and then rinse and repeat with another goal once an LLM has concluded that the previous goal was met. The next goal might be to fix unforeseen consequences of achieving the previous goal. See Ursula K. Leguin's "Lathe of Heaven".

> Built by whom? Acting as an 'agent' on behalf of whom?

Someone who didn't read the book.

An "agent" is just an LLM in for loop.

Exactly. And all it takes for an agent to "take initiative" is to not block the loop on user input at the very beginning.

Built by whom? Acting as an 'agent' on behalf of whom?