The notion that Yahusha Hamashiach would have spoke Greek based on business is not what he taught in the scripture. Yahusha, stated that he was about his Fathers business: Luke 2:
49 And He said to them, “Why did you seek Me? Did you not know that I must be about My Father’s business?”
The notion that the king would despise learning the language of people he hated is true:
This can also be said for Yahusha, why would he learn the language of a culture that were considered pagan and ungoldy? Why would he attempt to study their culture and language.
Even the followers of Christ were considered to be unlearned men, unlearned men would be known as not knowing Greek, Paul was the first figure that bible portrayed as being a learned man:
13 Now when they saw the boldness of Peter and John, and perceived that they were uneducated and untrained men, they marveled. And they realized that they had been with Jesus.
Paul's Education and Roman citizenship:
“I am a Jew, born in Tarsus of Cilicia, but raised in this city. I was educated at the feet of Gamaliel in strict conformity to the law of our fathers. I am just as zealous for God as any of you here today.
Now when the centurion heard this, he went and reported it to the chief captain, saying, "Do you realize what you are about to do? For this man is a Roman." And when the chief captain came up, he said to him, "Tell me, are you a Roman?" And he said, 'Yes.' (Acts 22: 25 - 27).
In all, Yahusha Hamashiach, would have equally have been resistant to learning from a culture that did not respect him or his people.
We also have to remember Christ refused to speak to the king:
8 When Pilate heard this, he was even more afraid, 9 and he went back inside the palace. “Where do you come from?” he asked Jesus, but Jesus gave him no answer. 10 “Do you refuse to speak to me?” Pilate said. “Don’t you realize I have power either to free you or to crucify you?”
11 Jesus answered, “You would have no power over me if it were not given to you from above. Therefore the one who handed me over to you is guilty of a greater sin.”
12 From then on, Pilate tried to set Jesus free, but the Jewish leaders kept shouting, “If you let this man go, you are no friend of Caesar. Anyone who claims to be a king opposes Caesar.”
13 When Pilate heard this, he brought Jesus out and sat down on the judge’s seat at a place known as the Stone Pavement (which in Aramaic is Gabbatha). 14 It was the day of Preparation of the Passover; it was about noon.
“Here is your king,” Pilate said to the Jews.
In all, why would God speak Hebrew and Aramaic throughout the Old Testament just to change his language in the New even when speaking to kings? Even in the Book of Daniel, God wrote letters on the wall that had to be translated, God doesn't change who he is for worldy kingdoms:
Therefore he sent the hand that wrote the inscription.
25 “This is the inscription that was written:
mene, mene, tekel, parsin
26 “Here is what these words mean:
Mene[e]: God has numbered the days of your reign and brought it to an end.
27 Tekel[f]: You have been weighed on the scales and found wanting.
28 Peres[g]: Your kingdom is divided and given to the Medes and Persians.”