There is an argument for the separation from the Roman Empire but it's not the points you are making. You are personifying an imperial state & statements like they didn't have respect for the latin empire is just plain wrong.

People who make the case it should be referred as the Roman Empire often give the argument that people themselves believed there was continuity & identified as Roman. What they forget is that historical naming conventions never take that into account, they are arbitrary dividing lines used to draw up history into manageable chunks & bring attention to significant monents of change, for example the decline of the Roman Republic. It's not a reference to people's identity.

However there is also a valid case to make that Byzantine Empire is a pejorative term that has too much negative baggage & should be discounted. The term itself has become an insult to refer to courts that are back stabbing, conspiracies & low morality. The consensus among historians is to refer to it as the Eastern Roman Empire & to do so at an earlier date, usually from Theodosius, to emphasise the continuity whilst still making the historical definition. Popular culture such as video games have not caught up with this however.

The exact definition of where you draw the line is difficult to identify clearly. It's not like the end of the Republic where we can draw a line when hereditary rule starts. Changes occur gradually by different emperors over hundreds of years. But there's no real need to be exact & articles with opinions on this are entertaining reads that anyone interested in the period would happily read so it's not exactly a problem. It's helped that Ancient Roman historians often get off the bus when he hit Constantine & the empire becomes Medieval in structure.

What we should really do, in my opinion, is make more divisions. Carve up the Roman Empire into several empires of different rise & falls. Harriet Flower has an excellent book that does this for the Republic arguing that Rome from a historian studying perspective had not a single republic but 6 distinct republics with definably different structures of govt, visible rises & falls and also experienced two interregnums where govt broke down.

Accepting that these lines are just divisions by historians & with that chopping individual periods up further would do alot to boost the study of those periods. For example historians look at Augustus's state and ask the question, how did the Roman Empire fall, they then start to talk about the Goths & migrations, disease, taxation still in the context of the Augustan Empire. This inevitably leads to historians giving all the change from Augustus to Honorius as a cause of the fall. This isn't correct, the question isn't framed right and should be always in the context of the Empire at the time which was very successful despite its differences. If we draw our lines here and say the Principate/Augustan Empire was its own distinct historical entity with a rise and fall that becomes easier then the smaller scope makes it easier to define. The Augustus Roman Empire fell during the crisis of the Third Century when the succession mechanism broke down. This line also gives us a nice valley for additional debate to flood. Maybe some revisionist historian wants to point out actually they can evidence it just took so many generations for inflation & economic damage to hit & succession wasn't a big part. Etc.

This is why we have these lines as historians & in my opinion the more the better.