Jesus, during His ministry, healed multiple people...a variety of individuals with all kinds of "unhealthiness". Everything from an unclean demon, high fever, various diseases, leprosy, paralysis, and a withered hand to those "at the point of death", those who had died, an unclean spirit, a disabling spirit, and dropsy (edema).
Soon afterward he went on through cities and villages, proclaiming and bringing the good news of the kingdom of God. And the twelve were with him, and also some women who had been healed of evil spirits and infirmities: Mary, called Magdalene, from whom seven demons had gone out, and Joanna, the wife of Chuza, Herod's household manager, and Susanna, and many others, who provided for them out of their means. (Luke 8:1-3 ESV)
I feel like I am one of those women (only I still pray for relief from my "thorn" (2 Corinthians 12:7-9)). Infact, had I been alive when God walked the earth, I believe whole heartedly I would have done as these women did.
Jesus had a heart for those who had faith...those who said, "Just say the words and there will be healing." He may not have experienced this type of affliction of the flesh (and hence not empathise), but He did feel compassion! And THAT is what I covet, His grace, mercy, and tenderness...and removal of ALL things "unhealthy" in my vapor (James 4:14) of a life.
"I tell you, my friends, do not fear those who kill the body, and after that have nothing more that they can do. But I will warn you whom to fear: fear him who, after he has killed, has authority to cast into hell. Yes, I tell you, fear him! Are not five sparrows sold for two pennies? And not one of them is forgotten before God. Why, even the hairs of your head are all numbered. Fear not; you are of more value than many sparrows. (Luke 12:4-7 ESV)