It is a commonplace among moderns that Emperor Constantine used the Christian faith for political leverage to unite the Empire. Certainly this was one effect of his actions, but if this had been his plan all along it would have been rather foolish. At the time of the Edict of Milan, Christians accounted for 15% of the population at most (nearly the same as blacks or Hispanics in the United States). Later Emperors, who lived in a more Christianized society are even less likely to have had purely Machiavellian motives.
While Justinian I certainly sought to politically unify the Empire and expand its territories, he also seems to have harbored a genuine zeal for Church unity. The Monogenēs hymn is purported to have been written as an (ineffective) overture to the monophysites. From the earliest imperial attempts to ensure unity (e.g. Constantine’s efforts to resolve the Donatist schism and the Arian controversy) through the later patristic era (e.g. Heraclius’ introduction of monothelitism, again seeking to woo the monophysites), the Emperors often had limited success. Still, they mostly seemed to have honestly held a concern for Christian unity in addition to more politically grounded motives. Justinian was wise to choose hymnody. In the end, the liturgical life of the Orthodox Church helped to bind together an imperial identity that no political propaganda could accomplish.
In his book, The Byzantine Legacy in the Orthodox Church, Fr John Meyendorff notes that the liturgy can be “considered as a tool of Byzantine cultural, religious, and to some degree, political expansion in the Middle East and throughout Eastern Europe. Indeed, the role of the liturgy [served] as a major—or perhaps the major—means through which Byzantine civilization was, on the one hand, maintained in the face of Islamic domination in the Middle East and, on the other hand, transmitted to the barbarians in the north and northwest[.]” Whatever unity the Emperors sought to establish and protect for the Church, she returned the favor in full, with interest.
Meyendorff further notes that in the West, growing notions of the monolithic authority of the papacy relegated the liturgy to a lesser semiotic role that was subject to ecclesiastical change by fiat, “whereas… Eastern Christianity visualized the liturgy as an independent authoritative source and criterion of faith and ethics.” He argues that Neo-Platonic thought accounts for this: The Byzantines saw the liturgy as the instantiation of a heavenly prototype, making the thought of “mere ritual” deviation unintelligible. I would argue that, in addition to this, the Byzantine attitude was also shaped by the need for unity. It provided what was needed, but was itself shaped by this need. Once outside an imperial context, liturgical diversity was not only given lip service (e.g. St Mark Eugenikos at Florence), but also put into practice by modern saints in quite distinct situations (e.g. St. Nektarios in the Pentapolis region of Egypt re-introducing St. Mark’s Liturgy, and St. John Maximovitch organizing the French Orthodox Church).