I mean, looking at the Albigensian Crusade it isn’t hard to picture the most zealous Catholics wanting to wipe out the heretics. It was a patently impossible idea, though—a handful of zealots couldn’t bring down Orthodoxy, let alone all of the varied flavors of Eastern Christianity.
The Roman invasion of Sicily did certainly put the fear of the Basileus into Italy and beyond—but in the long run I’d argue that was bad for Rome. That fear helped Giacomo Albizzi begin his unifying efforts in Tuscany, and in the long run paved the way for the unification of Italy as we know it. The Italian navy proved itself to be a huge thorn in Rome’s side on more than one occasion, not to mention its obscene economic power and influence.
Besides, it’s not like Rome held the parts of Sicily it conquered for more than two decades. They would’ve had better luck holding parts of the Italian boot proper, where IIRC there were some actual support for Rome among native Greek speakers.
I dunno, the Romans still controlled Bithynia and beyond at this point. Total Turkish conquest isn’t inevitable even in the wake of a nasty collapse of authority.
If some kind of unitary Turkish Empire was founded, I’d agree with your analysis. The Romans could hold them out of Europe proper with their navy, not to mention support from other Orthodox powers like Serbia.
The Roman Invasion of Sicily had a larger symbolic meaning. It was a sign that caused the Pope not to threaten the Roman Empire in any way. The war was started as a way to secure Sicily as a marriage gift demanded by the Emperor, giving his sister Helena to the Anjou King of Sicily. The possibility to invade Italy after all the humiliation since Basil II death put fear as far as Lisbon. The use of Turkish Soldiers proved its worth. The invasion succeeded in a decade.
At the end, it was more important to secure the Balkans after the Mongols left a vacuum there in the mid 14th century. Ruling Sicily without Moravian Serbia was a risky move anyway.
I'm more interested on how the Imperial Faction lost so much power to the Patriarch class in the "Century of the Patriarchy". The seven Emperors since Andronikos II to Basil V were weak as hell and the Patriarch of the Church had most of the Power. Could this have been avoided if the costly Italian War went better, rather than being crushed far in Lombardy?