The smooth transition of power from Queen Elizabeth II to King Charles III has been so uneventful as to provoke yawns from the rest of the world. Indeed, Britain has had fairly predictable and successful transitions of power ever since the Glorious Revolution of 1688.
The Byzantine Empire, on the other hand, held its breath almost every time an emperor died, and dozens of living emperors were ousted in violent overthrows. Perhaps the best example is the tragedy that befell Emperor Maurice (r. 582-602 AD). In 602, Maurice ordered his exhausted army to campaign north of the Danube during harsh winter. The troops refused, mutinied, proclaimed Phocas their leader, and demanded that Maurice abdicate. Then riots broke out in Constantinople, forcing the emperor and his family to flee the city on a warship. Phocas entered Constantinople and was immediately crowned emperor. His troops captured Maurice and his family and brought them to the harbour of Eutropius at Chalcedon.
On 27 November 602, the deposed emperor was forced to watch his five younger sons executed before he himself was beheaded. His wife, Constantina, and her three daughters were temporarily spared and sent to a convent, but in 605, after Constantina was convicted of a conspiracy against Phocas, they were all executed. The Persian Shah Khusrow II used this coup and the murder of his friend and patron as a pretext to launch a long war that exhausted and bled the two powers that they nearly collapsed during the subsequent Arab Conquest. And in a classic case of "what goes around, comes around," Phocas was overthrown in 610 by Heraclius and swiftly executed.
That's why the British so eagerly say, "Long live the King!"