Note those are two distinct explanations. OP's point about the speed of light explains only why we're not observing any civilization from the last 50,000 years,

Note those are two distinct explanations. OP's point about the speed of light explains only why we're not observing any civilization from the last 50,000 years, while the anthropic principle and the "quick, devouring species" assumption explain why no alien life exists at all in our past light cone.