I am going to go out on a limb and say there are no restrictions from traveling. He never even bothered to apply for visa’s and could arranged visas while traveling on His Irish passport before his renunciation. No one is minimizing the residential requirement of using a Tarc if they need to travel for business.
Nobody likes the requirement after naturalizing to be required to have a TARC and not get HHR and ID right away. After we have been living here for years before be do so. Obviously the rule could be changed as those like Fifefield who are are not required to use a tarc.
I like how Brian Jones quipped to me about did I know the difference between having a tarc and ID card. Well it was all covered in this thread from 2004.