There’s a lot of focus on whether the byzantines of 1444 are Rome or not. To me the answer is clearly “yes. But…”.
Someone made the comparison with modern day Britain, how it would be absurd to say that they’re no longer the same nation as the British empire. I buy this. But let’s say we’re creating an EU4: modern day. Should the old British Empire inspire the ideas for England (or for that matter, should they have ideas based around the simmering Anglo-Saxon/Norman conflict)? Should conquistadors and the high seas inspire the ideas for 2022 Spain? To me it seems much more logical that they should be based on what the nation is in the game’s time period. And Byzantium of 1444 (or Rome, if you like, though it seems more confusing than not), is not in this sense very similar to the Roman Empire of the early first millennium.
That said, should the byzantines have cool missions? Of course! Everybody should have cool missions, and their popularity makes them a logical choice. But honestly I’d rather see their missions guiding them towards reforming Rome (and make it slightly easier), then add content to Rome so any of the pretenders can use it.
Edit: for that matter, I think given advancements in mission tree technology, Rome should be rethought. It should be generally much easier to form (especially, but not exclusively, for Byzantium), and its ideas should be a bit worse (or maybe it shouldn't even have its own ideas, though I suspect that's a non-starter). But it should have a very large and interesting mission tree which makes up for the idea nerf with permanent modifiers IF the new Rome can actually match or exceed the accomplishments of the old.