The idea that Jesus was sent to specific people, and, that historically this is how God works, is, I believe, part of your answer, and accommodates our limitations.
Luke 4:17 And there was delivered unto him the book of the prophet Esaias. And when he had opened the book, he found the place where it was written, 18 The Spirit of the Lord [i]is[/i] upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised, 19 To preach the acceptable year of the Lord. 20 And he closed the book, and he gave [i]it[/i] again to the minister, and sat down. And the eyes of all them that were in the synagogue were fastened on him. 21 And he began to say unto them, This day is this scripture fulfilled in your ears. 22 And all bare him witness, and wondered at the gracious words which proceeded out of his mouth. And they said, Is not this Joseph's son? 23 And he said unto them, Ye will surely say unto me this proverb, Physician, heal thyself: whatsoever we have heard done in Capernaum, do also here in thy country. 24 And he said, Verily I say unto you, No prophet is accepted in his own country. 25 But I tell you of a truth, many widows were in Israel in the days of Elias, when the heaven was shut up three years and six months, when great famine was throughout all the land; 26 But unto none of them was Elias sent, save unto Sarepta, [i]a city[/i] of Sidon, unto a woman [i]that was[/i] a widow. 27 And many lepers were in Israel in the time of Eliseus the prophet; and none of them was cleansed, saving Naaman the Syrian. 28 And all they in the synagogue, when they heard these things, were filled with wrath, 29 And rose up, and thrust him out of the city, and led him unto the brow of the hill whereon their city was built, that they might cast him down headlong. 30 But he passing through the midst of them went his way, 31 And came down to Capernaum, a city of Galilee, and taught them on the sabbath days.
Mark 3:1 And he entered again into the synagogue; and there was a man there which had a withered hand. 2 And they watched him, whether he would heal him on the sabbath day; that they might accuse him. 3 And he saith unto the man which had the withered hand, Stand forth. 4 And he saith unto them, Is it lawful to do good on the sabbath days, or to do evil? to save life, or to kill? But they held their peace. 5 And when he had looked round about on them with anger, being grieved for the hardness of their hearts, he saith unto the man, Stretch forth thine hand. And he stretched [i]it[/i] out: and his hand was restored whole as the other. 6 And the Pharisees went forth, and straightway took counsel with the Herodians against him, how they might destroy him. 7 But Jesus withdrew himself with his disciples to the sea: and a great multitude from Galilee followed him, and from Judaea, 8 And from Jerusalem, and from Idumaea, and [i]from[/i] beyond Jordan; and they about Tyre and Sidon, a great multitude, when they had heard what great things he did, came unto him. 9 And he spake to his disciples, that a small ship should wait on him because of the multitude, lest they should throng him. 10 For he had healed many; insomuch that they pressed upon him for to touch him, as many as had plagues. 11 And unclean spirits, when they saw him, fell down before him, and cried, saying, Thou art the Son of God. 12 And he straitly charged them that they should not make him known. 13 And he goeth up into a mountain, and calleth [i]unto him[/i] whom he would: and they came unto him.
Acts 3:1 Now Peter and John went up together into the temple at the hour of prayer, [i]being[/i] the ninth [i]hour[/i]. 2 And a certain man lame from his mother's womb was carried, whom they laid daily at the gate of the temple which is called Beautiful, to ask alms of them that entered into the temple; 3 Who seeing Peter and John about to go into the temple asked an alms. 4 And Peter, fastening his eyes upon him with John, said, Look on us. 5 And he gave heed unto them, expecting to receive something of them. 6 Then Peter said, Silver and gold have I none; but such as I have give I thee: In the name of Jesus Christ of Nazareth rise up and walk. 7 And he took him by the right hand, and lifted [i]him[/i] up: and immediately his feet and ankle bones received strength. 8 And he leaping up stood, and walked, and entered with them into the temple, walking, and leaping, and praising God. 9 And all the people saw him walking and praising God: 10 And they knew that it was he which sat for alms at the Beautiful gate of the temple: and they were filled with wonder and amazement at that which had happened unto him.
I wonder if Jesus was concerned for the safety of those whom He had healed or delivered?
John 7:13, John 19:38, John 20:19