"It is quite clear from this passage that Jesus came for Jews and non-Jews alike."
No, he didn't. It was Paul who took Christianity to the Gentiles, and Paul didn't know Jesus. Jesus ministered to the poor Jewish masses. He criticized the Gentiles while doing so. He hesitated to help the Syro-Phoenician woman, suggesting non-Jews were 'dogs', begging for His 'crumbs'. Yes, He spoke to a handful of Gentiles, and helped a few, but he was Jewish, and ministered to Jews, almost exclusively. I'm talking about what Jesus actually DID, as opposed to the extensive commentary on it, found in the many books of the New Testament. All that is interpretive 'layering' stacked onto His basic story, by scribes who came afterward, scribes who didn't know Jesus, some of whom probably weren't even alive during His lifetime and ministry. When you focus on what he actually DID and SAID, according to the Gospels, it becomes clear: JESUS WAS A JEWISH TRIBALIST.
What about that story he said about the Good Samaritan? That was pretty critical of a tribe of Israel.
Or one of my favorite passages Matthew 5-12:
5And when Jesus was entered into Capernaum, there came unto him a centurion, beseeching him,
6And saying, Lord, my servant lieth at home sick of the palsy, grievously tormented.
7And Jesus saith unto him, I will come and heal him.
8The centurion answered and said, Lord, I am not worthy that thou shouldest come under my roof: but speak the word only, and my servant shall be healed.
9For I am a man under authority, having soldiers under me: and I say to this man, Go, and he goeth; and to another, Come, and he cometh; and to my servant, Do this, and he doeth it.
10When Jesus heard it, he marvelled, and said to them that followed, Verily I say unto you, I have not found so great faith, no, not in Israel.
11And I say unto you, That many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven.
12But the children of the kingdom shall be cast out into outer darkness: there shall be weeping and gnashing of teeth.
Yes lets actually talk about what Jesus actually said.