You generally don’t need it on carbon bars as most come with a coated and roughed up center section for the stem. Your grips, brakes, etc don’t need much pressure to get a solid grip on the bars so you don’t need it there.
You shouldn’t put it on a carbon steerer either as it can get into the headset bearings and ruin them, and potentially cut I to the steerer.
Only place you really need the carbon paste is a seat tube in a carbon frame as the lower clamping pressure might result in post slippage under your weight. I also use it on my roadbike infinite angle seat post to stop it slipping nose down (or up).
Worth having a tube of paste though as it’s handy, cheap, and needs to be replaced from time to time in your seat post.