Let's say that the Gothic War is a lot shorter ITTL (say it lasts "just" five years instead of almost twenty) so that, by the 550s, the Eastern Roman Empire's finances are in much better shape despite the plague. Because of this, they are considerably more successful in their invasion of Visigothic Spain, not stopping near Córdoba but instead marching all the way to the Duero, the Pyrenees and maybe even Septimania if the Franks don't get there first.
What would be the effects of a much larger Provincia Spaniae? Would there be major rebellions against Constantinople's authority, or would most of the population and clergy there in particular be glad they're not ruled by Arians anymore? Would the place become a source of revenue to the empire, or is it just too far away and with too many powerful local notables to be controlled effectively at this point? Would the place be divided into smaller provinces, or become one giant Exarchate like Africa and Ravenna? Would the Franks stir up trouble (I assume they'd want to take Septimania and maybe Catalonia after that)? Would it become a source of usurpers, like Heraclius and Gregory the Patrician in Africa?
Lastly, could a longer lasting and more thorough reconquest of the west make the empire as a whole be less Greek and more Latin in character? Would the Pope become completely subordinate to the emperor, much like the Patriarch of Constantinople? What about the Roman Senate, which was devastated by the long Gothic War and would likely at least last longer ITTL?
What would be the effects of a much larger Provincia Spaniae? Would there be major rebellions against Constantinople's authority, or would most of the population and clergy there in particular be glad they're not ruled by Arians anymore? Would the place become a source of revenue to the empire, or is it just too far away and with too many powerful local notables to be controlled effectively at this point? Would the place be divided into smaller provinces, or become one giant Exarchate like Africa and Ravenna? Would the Franks stir up trouble (I assume they'd want to take Septimania and maybe Catalonia after that)? Would it become a source of usurpers, like Heraclius and Gregory the Patrician in Africa?
Lastly, could a longer lasting and more thorough reconquest of the west make the empire as a whole be less Greek and more Latin in character? Would the Pope become completely subordinate to the emperor, much like the Patriarch of Constantinople? What about the Roman Senate, which was devastated by the long Gothic War and would likely at least last longer ITTL?