According to Suetonius, Caesar said to Marcus Brutus, in Greek, "And you, my child?" (kai sy, teknon).
Maybe Shakespeare thought his audience might be able to make sense of a three-word phrase in Latin but would be totally lost hearing Greek. (Of course, the saying "it was Greek to me" comes from the same play.)
I decided to read the rest of the article and found this:
“For one, we know who the soothsayer was and what he really said: he was named Spurinna, and he was from Etruria. That’s important, because Etruscans were known to specialize in divination. Cicero’s letters , Plutarch, and Suetonius all confirm his high status. As notably, Spurinna’s warning to Caesar was more complex — and more accurate — than the type of prophecy most modern skeptics would dismiss. “They have a lot of contacts,” Strauss says, “and they’re people who know what’s going on.” That would have made Spurinna’s prophecy a more frightening bellwether of the anti-Caesar sentiment in Rome. Soothsayers could poll the elites, and the elites did not like Caesar.
On February 15, Spurinna said he found a bad omen: a bull without a heart (it’s unclear if the bull was a genetic abnormality, a shocking sign, or a soothsayer’s poetic license). After that, Spurinna told Caesar to beware for the next 30 days, not just on the Ides of March. It wasn’t a lucky prediction but rather a calculated assessment of Rome’s political climate. The end date of the prophecy wasn’t a coincidence, either — on March 18, Caesar was going to embark on a multiyear military campaign that would take him away from Rome. The assassins had to kill him before he left.”
Thus, there were large numbers of veteran soldiers in and around Rome looking forward to going off to Parthia with Caesar with paydays, looting, etc. If, in fact, Cassius believed this was foolishness, then that would explain why he was not able to win them over.
It is very important to bear in mind that Shakespeare was writing against the backdrop of his time. This was written late in the reign of Elizabeth I, of the Tudor dynasty. The public was acutely aware of thirty years of bloody civil war during the Wars of the Roses. The Tudor dynasty had brought relative peace. So, a theme that would resonate in his day was the dangers of regicide and civil war and the importance of smooth transition of power. Remember, Elizabeth did not have an heir, which caused considerable anxiety.
The English were very fond of the story of Rome and identified with the Romans. The fall of the Republic did not in the 16th Century trouble them in that they had always been governed by a monarch and Parliament that in their eyes roughly corresponded with the Senate. That view later changed, of course.