There are a couple dozen mentions of Jesus touching people when he healed them. The healing Jesus did was personal, one-on-one.
There are only two cases I can come up with of Jesus healing someone long distance: The centurion whose beloved servant was deathly ill recognized that Jesus could heal with a word (Luke 7:1-10). The Canaanite woman whose daughter was ill went to Jesus asking for healing but didn’t bring her daughter, clearly believing Jesus could heal from any distance (Matthew 15:22-28). Both Gentiles, and both highly praised by Jesus for their exceptional faith.
What we don’t ever see is a mass healing. Never. Even when there are many people seeking healing, he healed them one by one. (For example Mark 1:32-34.) Almost certainly he touched each one—he stayed in the house while the crowd was at the door, meaning that at most one family group could get in at a time. Jesus’s healing was personal, individual. As it still is today.
And here’s something else. We see Jesus touching the dead: He takes Jairus’s daughter by the hand and raises her from the dead (Luke 8:41-56). He also touches the bier of the widow of Nain’s son to stop the funeral procession, and raises the dead man (Luke 7:11-15). Both of these constitute contact with the dead.
On his way to raise Jairus’s daughter, Jesus is touched by a woman with hemorrhage, and she is healed. A person with a hemorrhage was unclean, and so was anything and anyone they touched. And a leper kneels before Jesus and says, “Lord, if you will, you can make me clean.” Then, both Matthew and Mark report, “Jesus stretched out his hand and touched him, saying, ‘I will; be clean.’ “ (Matthew 8:2-3) Jesus could have just said “I will, be clean”, but he makes a point of touching him first, and then says it.
All these touches should have made Jesus unclean; the Law explicitly says so! But no one so much as suggests that he has become unclean! Under the Law, uncleanness is spread by touch, and holiness isn’t (Haggai 2:12-13) But the power of Jesus is such that the tide is reversed! Uncleanness is not rubbed off on him. Instead, it’s pushed away so what was once unclean now isn’t.
When Jesus touches the unclean, it doesn’t defile him. When he touches us (spiritually), he heals us—so we are no longer unclean from sin. We are made as though we had never been unclean at all. “If you are willing…” When we ask, he is always willing; he reaches out and touches us. He is not defiled. And we are healed.