Exactly! Funny thing is, Irene nearly married her contemporary Charlemagne. Had this been done, he would have moved from Aachen to Constantinople, united his empire with her's and possibly recreated the Roman Empire in some form. Of course, she was deposed before this could happen, and in any event, the two empires were too different to really cohere well; one was Latin/Germanic and Catholic, the other was Greek and Orthodox. It would have taken a long line of superb emperors, excellent luck, reconciliation between the Catholic and Orthodox churches, and a serious opening up and building/rebuilding of the Western European infrastructure and economy to match Byzantine standards in order rebuild the empire, and even then, it would have been a Christian state, not the old Rome of the Caesars.
Your turn, Mirumoto_Kenjiro.