I was informed the Concorde was the only supersonic airliner that could supercruise- cruise supersonically on jet thrust without afterburner. The TU144 needed constant reheat to maintain supersonic cruise, with all the fuel gulping that implies. So....carry any sort of payload Moscow-Havana? Nahhh! Fuel tankage to do it subsonic across Europe then supersonic with a payload of 2 people? No chance. If it ever did it, it would have had to be subsonic with hardly any payload.
I seem to recall it was only ever used on one internal service (Alma Ater or somewhere obscure?) for a while before being quietly withdrawn to await NASA testing.