You may have original songs and your favorite covers memorized, but the moment the live stream begins and you play the final chord or sing the final note of your first song, you don't want to waste time trying to remember what song you wanted to play next in case your mind goes blank.
Think of it this way, too: your setlist can be a frame of reference. It doesn't mean you're completely locked in. You can always call an audible if another tune comes to your mind.