Essentially, why wasn't the Kingdom of Greece considered a continuation of the Roman/Byzantine Empire?
there was a lot of pressure from outside sources for the Greek revolution against the ottomans to be seen as the rise of classical Greece rather than the reestablishment of the eastern roman empire. Greeks themselves at the time called themselves romans or at least many of them did, but all the volunteer British etc from other countries were very much caught up in the homeric history rather than the byzantine and it was worth courting their support. I'll let this response stand till someone can come by with the sources. I'm in an airport at the moment so nothing at hand.