I disagree. It makes just as much sense as any other flip on spawn.
Why? Most historical equivalents of flips were caused by ethnic similarities or conquest upon existence. If China founds a city in Japan, it would be assumed that the small amount of Chinese population would assimilate with the locals, and it would want to join a united nation of that ethnicity. However, Byzantium was not a new ethnic group or nationality coalescing, it was merely a civil division of the Roman Empire. Most people in both halves considered themselves Romans, and the division as merely a political one to manage a new system. When Western Rome collapsed, the Eastern half was known as the Roman Empire, because that's what it was when it was originally started.
Reasons for flips to a civilization fail to make sense in the context of the Byzantines.
-Ethnic/national bond: For previous Roman territories, they would become Byzantine because the Roman Empire would be split in two. However, the only bond uniting the Romans (and Byzantines, to this extent) was the fact that they were governed by a greater power; Rome (later Constantinople). There was no "ethnic Byzantine identity", the national identity of the Byzantines was at first Roman and later Christian.
-Hasty conquest: The creation of the Eastern Roman Empire was done by dividing the existing empire in half to make maintaining a large empire less of a problem. At this point in Roman history, Rome was not expanding at all, it was contracting, and thus no conquests were made by the Byzantines during the beginning of their existence with the exception of a few border clashes with the Sassanids, but that problem had existed with the united empire as well.
Therefore, for the above reasons, the Byzantines should only flip Roman cities.