“When Jesus went out He saw a great multitude; and He was moved web compassion for them, and healed their sick.” – Matthew 14:14
Jesus can and has healed people of physical ailments. “And there was a woman who had had a discharge of blood for twelve years, and though she had spent all her living on physicians, she could not be healed by anyone. She came up behind (Jesus) and touched the fringe of His garment, and immediately he discharge of blood ceased.” (Luke 8:43-44)
Jesus’ main purpose of the healing is to bring about life change – to cleanse from sin. “And when Jesus heard it, He said to them, ‘Those who are well have no need of a physician, but those who are sick. I came not to call the righteous, but sinners.’ ” (Madk 2:17) Because Jesus came to save, He did not save Himself from the punishment of the cross, though that was within His power to do.
Unfortunately, many did not recognize their need for Him (nor do many even today!), but that did not stop Him. He promised that His message would not be widely received. “And He said to them, ‘Doubtless you will quote to Me this proverb — Physician, heal yourself. — What we have head you did at Capernaum, do here in Your hometown as well.’ And He said, ‘Truly I say to you, no prophet is acceptable in his hometown.’ ” (Luke 4:23-24)