I have read translations of the surviving Acta of the Seven Councils, and the Papal Legates did not preside — for instance, at Chalcedon, in the first session they addressed themselves to “your holiness” (not plural, but singular, indicating the Patriarch chairing the session) and the third session was not opened by the Legates, but by an Archdeacon of the Patriarchate of Constantinople, presiding in place of the Patriarch, while at the Seventh, it is absolutely clear that Patriarch Tarasius of Constantinople presided.
“Caesaro-Papism!” I get a belly laugh every time I hear that Latin myth mentioned.