The British can't just do whatever they want, you know. Assuming the British come knocking at the same time they did OTL, Egypt will have been a core Roman province for around 1900 years. It is not some impoverished indebted colony to be traded from one power to another. It would be akin to the British annexing Normandy in 1900 -- it would be absurd. And I don't know why you keep talking as though the Romans have to take Egypt. They don't have to take anything, Egypt had been under Roman control since 30 BC, only being lost after the Arab invasions, which were repelled according to the author's post.Yes but as soon as we get into the modern period it becomes harder and harder to do so considering outside interference. Britain would probably protect Egypt for the sake of a canal.
While Byzantium can take Egypt before the modern period I think it's a bit frivolous and means they'll have to extend their military forces over quite a bit rather than keeping it largely limited to the two fronts of Anatolia and the Balkans meaning that if there were to be some devastating event it'll hurt all the harder.
And maintaining control over Egypt is anything but frivolous. It is the granary of the empire, a major source of manpower and taxes, and the seat of the Alexandrian Patriarchate. For the Romans, control over Egypt provides far more benefits than it does drawbacks.