I know that the excuse was that empress Irene was not a man, hence the throne of Eastern Roman Empire was allegedly empty. But by what right pope could crown the emperor? Was there any legal foundation to this or was it just an outcome of a power struggle between Franks, Byzantines and pope (usurpation)?
It had a legendary precedent with the crowning of Constantine by Sylvester the 2nd (I would be glad if someone could confirm if this legend was not created after the reign of Charlemagne). In addition, the Byzantine emperors were crowned by the Patriarch of Constantinople, wich is the equivalent of the pope, for the Orthodox church. But there is a little difference, has in the Byzantine ritual, the emperor was praised by the population and called emperor by the people before the coronation. The Pope Leo put the crown on the head of Charles before any acclamation, making the Pope an indispensable element in the western imperial coronation ceremony.