Why are centurions featured so frequently in the New Testament?
There are several reasons for this, that make sense historically speaking.
A centurion was a Roman officer and often had important social status and held powerful positions in society. Generally speaking a centurion commanded about either 30, 60,100 or even more men within a Roman Legion, depending on circumstances.
A centurion's symbol of office was the vine staff, with which they disciplined even Roman citizens, who were otherwise legally protected from corporal punishment by the Porcian Laws. Centurions also served in the Roman navy. After the 107 BC Marian reforms of Gaius Marius, centurions were professional officers. In Late Antiquity and the Middle Ages, the Byzantine army's centurions were also known by the name kentarch (Greek: κένταρχος, translit. kentarchos).
In the Roman infantry, the centurions commanded a centuria or "century". During the Mid Republic these centuries were grouped in pairs to make up a maniple, each century consisting on 30 - 60 men. After the Marian reforms a century typically composed of around 80 men, with six such centuries forming a legionary cohort. Later, generals and emperors further manipulated these numbers with double and half-strength units. Julius Caesar, for instance, made the first cohort of 5 double strength centuries.
Centurions received a much higher rate of pay than the average legionary. Veteran legionaries often worked as tenants of their former centurions.
Unlike legionaries, the Roman Centurions carried their swords on their left side as a sign of distinction and carried the pugio (dagger) on the right, as the sidearm.
Centurions often had important social status and held powerful positions in society. They seem to have received their status according to their rank. On retirement, they could be eligible for employment as lictors. - Centurion
Thus we can see why Roman centurions were mentioned often in the New Testament.
It was a Roman centurion who confessed that Jesus was the Son of God at the Crucifixion, as he was in the forefront of the execution of Jesus!
Now when the centurion, and they that were with him, watching Jesus, saw the earthquake, and those things that were done, they feared greatly, saying, Truly this was the Son of God. - Matt 27: 52
It was also to the centurion of Jesus’ crucifixion that Pilate asked information about the actual death of Jesus.
…43Joseph of Arimathea, a prominent Council member who himself was waiting for the kingdom of God, boldly went to Pilate to ask for the body of Jesus. 44 Pilate was surprised to hear that Jesus was already dead, so he summoned the centurion to ask if this was so. 45When Pilate had confirmed it with the centurion, he granted the body to Joseph.… - Mark 15: 44
Seeing that Roman centurions were men of importance within the Roman Army, it is not surprising that that they the could have great influence in helping spread the Gospel.
The Faith of the Centurion
5 When Jesus had entered Capernaum, a centurion came to him, asking for help. 6 “Lord,” he said, “my servant lies at home paralyzed, suffering terribly.”
7 Jesus said to him, “Shall I come and heal him?”
8 The centurion replied, “Lord, I do not deserve to have you come under my roof. But just say the word, and my servant will be healed. 9 For I myself am a man under authority, with soldiers under me. I tell this one, ‘Go,’ and he goes; and that one, ‘Come,’ and he comes. I say to my servant, ‘Do this,’ and he does it.”
10 When Jesus heard this, he was amazed and said to those following him, “Truly I tell you, I have not found anyone in Israel with such great faith. 11 I say to you that many will come from the east and the west, and will take their places at the feast with Abraham, Isaac and Jacob in the kingdom of heaven. 12 But the subjects of the kingdom will be thrown outside, into the darkness, where there will be weeping and gnashing of teeth.”
13 Then Jesus said to the centurion, “Go! Let it be done just as you believed it would.” And his servant was healed at that moment.
Let us not forget the encounter of the Centurion Cornelius with St. Peter.
Cornelius Calls for Peter
10 At Caesarea there was a man named Cornelius, a centurion in what was known as the Italian Regiment. 2 He and all his family were devout and God-fearing; he gave generously to those in need and prayed to God regularly. 3 One day at about three in the afternoon he had a vision. He distinctly saw an angel of God, who came to him and said, “Cornelius!”
4 Cornelius stared at him in fear. “What is it, Lord?” he asked.
The angel answered, “Your prayers and gifts to the poor have come up as a memorial offering before God. 5 Now send men to Joppa to bring back a man named Simon who is called Peter. 6 He is staying with Simon the tanner, whose house is by the sea.”
7 When the angel who spoke to him had gone, Cornelius called two of his servants and a devout soldier who was one of his attendants. 8 He told them everything that had happened and sent them to Joppa.
Thanks to a centurion, St. Paul’s life was spared at Malta!
…42The soldiers planned to kill the prisoners so none of them could swim to freedom. 43But the centurion, wanting to spare Paul’s life, thwarted their plan. He commanded those who could swim to jump overboard first and get to land. 44The rest were to follow on planks and various parts of the ship. In this way everyone was brought safely to land.…
Obviously Roman Centurions were men of great influence!
A historical reenactor in Roman centurion costume. Note the transverse crest on the Galea (helmet). It was worn to indicate the wearer's rank in regimental 'triumph' and honorific parades. Its purpose was purely symbolic. It was not part of the standard battle-dress of Roman soldiers in the field.