Why do people assume that the title of Roman Emperors was a single word?
Is President Trump's title "President" or "President of the United States"? Since the title is abbreviated POTUs I would guess it is a phrase.
The president of the United States (POTUS)[B] is the head of state and head of government of the United States of America. The president directs the executive branch of the federal government and is the commander-in-chief of the United States Armed Forces.
So Wikipedia seems to think the title is a phrase.
Is the title of Elizabeth II a single word or a phrase?
Since 1953 her title in the United Kingdom has had an English version and a Latin version, which are not, repeat not, exact translations:
In English: Elizabeth the Second, by the Grace of God of the United Kingdom of Great Britain and Northern Ireland and of Her other Realms and Territories Queen, Head of the Commonwealth, Defender of the Faith18
In Latin: Elizabeth II, Dei Gratia Britanniarum Regnorumque Suorum Ceterorum Regina, Consortionis Populorum Princeps, Fidei Defensor
So many present titles are phrases. Some may object that by "title" they specifically mean the single word that describes the rank or position or function of the leader, and not the complete phrase that describes both the type of leadership and also the group that is led.
Even accepting that argument, there are plenty of examples of ranks, positions, or functions that are described by phrases and not by single words.
For example, "Chairman of the Board of Directors of General Motors", "Chairman of the Presidium of the Supreme Soviet of the Union of Soviet Socialistic Republics", "Grand Duke of Lithuania", "Vice Admiral", "Field Marshal", "First Class Boy", "Grand Prince of Kiev", "Grand Master of the Teutonic Knights", "Cardinal Deacon", "Nagusa Nagast" meaning "King of Kings", etc., etc.
The early Roman emperors used a number of separate powers, titles, and honors. Their main titles included Imperator, Caesar, Augustus, and Princeps.
There are examples of an Imperator Caesar Augustus having authority over a lesser ruler or designated successor with the title of Imperator Caesar, so one could say that in the Roman Empire Imperator Caesar Augustus meant "emperor", or "senior emperor", and Imperator Caesar meant "emperor's heir" or "junior emperor".
Therefore, I am somewhat skeptical that a single Latin word meant "emperor", and tend to think that the three word phrase Imperator Caesar Augustus meant emperor.
The titles used by the Holy Roman Emperors varied t lot over time.
By about 1190 the title of a man elected emperor but not yet crowned in Rome by the pope was:
Romanorum Rex semper augustus
"King of the Romans always Emperor/Imperial".
And after being crowned in Rome by the Pope the title became:
Romanorum Imperator et semper augustus
"Emperor of the Romans and always Emperor/Imperial".
In the later middle ages semper augustus was mistranslated in the German versions of the title.
Romischer kayser zu allen zeyten merer des reichs
There Caesar instead of imperator or augustus, or all three together, is translated into German as kaiser, and semper augustus, meaning "always emperor" or "always imperial", is mistranslated into German as zu allen zeyten merer des reichs, meaning "in all times enlarger of the realm", or "perpetual enlarger of the empire".
The last major change in the imperial title came when emperors stopped going to Rome to be crowned and took the imperial title immediately after election and coronation in Germany.
Electus Romanorum Imperator semper Augustus, ac
"Elected Emperor of the Romans, Always Emperor (or always Imperial), and King in (or of) germany".
erwählter Römischer Kayser, zu allen Zeiten Mehrer des Reichs,
in Germanien.... König,
"Elected Emperor of the Romans, in all times Enlarger of the Realm, King in Germany".
In my opinion emperor, empereur, emperador, imperador, etc. based on imperator, and kaiser, tsar, etc. based on Caesar are equally valid or invalid words for emperor, since they are all single words based on single words that are part of the full phrase imperator caesar augustus which might be considered necessary to fully give the title of the Roman emperor. The fact that the Holy Roman Emperors believed themselves to be Roman emperors is why they often and usually used both imperator and augustus in their Latin titles.
Of course the single words like "emperor", kaiser, and tsar, etc., etc., are quite sufficient for the lesser 18th, 19th and 20th century monarchs of Russia, France, Austria, Haiti, Mexico, Brazil, Germany, India, Bulgaria, and Central Africa, showing that in rank they were some sort of "sub emperors", at least one rank lower than the Roman, "Byzantine" and Holy Roman Emperors.