The Romans did not choose to have an emperor rather than a republic. The change in political system was the result of the Roman Republic coming to an end as a result of the civil wars which tore it, and Rome, apart. Augustus emerged as the final Victor of these wars. He gained control of the Roman legions and accumulated a massive wealth through the spoils of war.
Augustus used his military power and his wealth to establish his own absolute personal rule and became the first Roman emperor. The Romans acquiesced with this because they were left exhausted by the wars, there was a power vacuum which Augustus filled and because he was the adoptive son of Caesar. The people wanted a strong government which could restore stability and hoped that Augustus would continue Caesar's reforms in favour of the poor.
Your question is rather vague. If you are referring to the Romans, it was the emperor Diocletian.
Their territory was too large to govern by democracy
The political thinking of the time was that the Romans never wanted to be subject to the whims and orders of a one man rule. They established the republic to avoid this and to give the people a voice in how they were governed. This concept is reflected in the USA which has since creation been a republic rather than a democracy.
Ancient Rome had three types of leaders. In the time of the Roman Kingdom, it had a King; in the time of the Roman Republic, it had two Consuls for the majority of the time, and a Dictator in times of emergency; and in the time of the Roman Empire, it had figures now generally referred to as 'emperors', who held various titles (i.e. Augustus and Princeps).
Were the Romans from Greece? No, they were from Rome, which is a city of Italy. Hence, Romans rather than Greeks.
No one in the US adopted all of the political ideas of the Romans. The fathers were inspired by the Roman Republic, but did not adopt the ideas of this republic because this political system applied to an ancient society, which was totally different. They were strongly influenced by Montesquieu, am 18th century French philosopher , rather than the Roman political system.
The Roman monachy was not a hostory of 244 years of harsh rule. Only its last king was a tyrant. The Romans overthrew the last Roman king in a rebellion in 509 BC because he was a tyrant. They decided to do away with the monarchy and establish a republic to prevent the return of tyranny. Monarchy became associated with tyranny. They created the Roman Republic, which was headed by two annually elected consuls. Having two men in charge meant that they could counterbalance each other. The short term of office ensured that no one could concentrate power in his hands and thus become a tyrant. The Romans also swore that they would not let anyone try to become a king. Trying to become a king was the worst possible accusation .In the 5th century BC one man was killed and his house destroyed and in the 4th century BC another man was executed because of accusations of trying to become a king.
After Augustus became emperor the power and authority was invested in one person rather than a collective body. The outward appearances of the republic were maintained, such as the various offices, but the real power was in the hands of the princeps, or first citizen, who was the emperor. Because he had the power of a tribune, he could veto any legislation not to his liking.
Rather Naughty
Actually, China is a republic. A republic is a state governed by the people or their elected representatives. Although China is a one-party Communist authoritarian state, which has what most republics consider to be a repressive government and does not tolerate dissent, it qualifies as a republic because it has a President ( currently Xi Jinping ) rather than a monarch or emperor.
Texas became better known as the "REGION", rather than the republic of Texas.
Two consuls meant two opinions, so no judgment is completely bias. Although, even with two consuls, corruption can be present at certain times...