This may have been a way of making a social comment about English society - but playing safe with the idea that would have been dynamite. Much safer for a bard's head to have the comments take place miles away in a another country.... and of course it's a great story anyway in terms of a history.
There were rumors in Caesar's time that the people in Rome wanted a king and some thought that Caesar wanted to be the main man and be king himself! Plutarch commented that this was what made him unpopular. They remonstrated with him but began to get more alarmed when it looked like he was a control freak who wouldn't listen or 'debate' - a discussion idea that the Romans were very fond of. At last one small group decided there was only way ... and planned to kill him. The concensus got larger so that by the time Caesar sought aid in the group - none was forthcoming as even some of his friends were in on it. Caesar knew the game was up... an opportunity for a cautionary tale against becoming power-mad that Shakespeare couldn't resist as a safe comment on his time?
The obvious answer is that Rome is the actual place of Caesar's assassination, and Shakespeare--while he takes some historical liberties--does try to present the assassination and the preceding/following events relatively realistically. He consulted Plutarch's Lives for the play.
Symbolically, the political issues and Shakespeare's discussion of chaos's negative effects upon individuals and empires fits Ancient Rome's political arena. The idea of individuals fighting for ultimate power (Caesar or a king) against a republic government not only occurred in Rome, but it gives Shakespeare and opportunity to discuss how these same issues affect the British Empire. Moreover, Shakespeare portrays the commoners in Rome as clamoring for a king, and uses the far-away setting to hint at how his own people should feel about their own kings and queens.