If you think "Greek Fire" is the only thing Byzantium has to offer, then your knowledge on the subject appears to be painfully limited. Cataphracts, Basilica's, The Patriarchate, Theodosian Walls, the Macedonian Renaissance, the Komnenoid Restoration, the Bulgaro-Byzantine Wars, there's plenty to choose from, an all of the above apply to Byzantium and not to Rome.
Increased flavor differences between Athens/Sparta, India/Maurya and Angevin Empire/Great Britain/Valois France would be greatly appreciated though. It really goes beyond one ability + a different colours scheme + a separate capital. Different symbols and city lists (Eleanor settling industrial era cities such as Bradford and Stoke-upon-Trent triggers my inner aspie) could go a long way, as would a unique component (Give Perikles a unique Pentekonter instead of the Hoplite, give Gandhi Sepoys or Gurkha's instead of the Varu, give Eleanor a Troubadour Unique Unit (replacing the Rock Band but available at medieval faires) over the Sea Dog/Garde Impériale). The current Alt leader system is a step in the right direction imo, but it's only halfway where it should be.
* Cataphracts - not uniquely Byzantine and were imo a poor choice of unique in V. Also, we already have plenty of horseys for Poland, Russia, and Hungary just next door.
* Basilica - so, like a sad shadow of the lavra which would better fit the Byzantines?
* Theodosian walls - do we really need another wall unique?
This is my point. Yes, Byzantines have things to build uniques from but none of them are particularly good options. There are too many civs that have cannibalized Byzantium's already limited design space. If we got basilica and cataphract, it would basically be a tanky Russia clone.
The core of this problem is that Eastern Europe, despite being ethnically fractured, is really just a homogenous continuum of slight variations on the same history. Christianity and cavalry. There are only so many mechanical ideas you can pull out of the same taffy, and to my mind (and it seems the devs' mind) Byzantium is not as high priority as representing Poland and Russia (and the Ottomans) first. And now Georgia and Hungary, apparently. And while I completely see your point that a Byzantine alt leader wouldn't do justice to later Byzantium, I personally don't think later Byzantium has much new to offer to VI mechanically or aesthetically at this point. It might have had potential, were it added sooner, but it will never be a priority in any civ game because it's not a wholly distinct polity and culture like Russia, or Poland, or the Ottomans. It's still, to some extent, just "Rome, again," and that is why it will always be a filler civ that just barely makes it in after all the other ideas are explored. This rule so far holds true for VI.
So, again, someone is going to be dissatisfied with how the devs approach this no matter what happens. Because there are those like you who consider it a "staple" and want it given the full glory treatment. And there are those like me who consider it "filler" and don't see any space that needs filling. Neither is precisely wrong, but the devs are only going to take one side on this issue, and at this point we don't know.
I do think that if they go with Theodora, who is the clear frontrunner, she should just be an alt leader for Rome. She is a terrible leader for the proper "Byzantium" proposed by everyone and I think most would agree. And the Rome uniques, while not fitting "Byzantium," would adequately represent Rome under her.
I agree that leaders could stand to be differentiated a bit better. Like give each leader their own unique. Several already have them and there are some instances where they practically have one (like Jaya and the Baray). But I would still rather have alternative civ ideas represented this way rather than as full civs.