Well I for one have interest in Catholic Byzantium. This hasn't been much explored, but Thomas Palaiologos had reasonably good connections with the Pope and with Genoa, so something at least ought to come of that in a fantasy scenario. Interesting story arcs could be developed with a resurgent Byzantium getting enmeshed in the politics of Italy alongside France and Austria, for example.
In addition, a Catholic resurgent Byzantium might, once they had shown themselves as winners, be able to get at least some meaningful support from the Pope, the Italian naval powers, and the Spanish in campaigns against the Turks.