Compassion means Action
Sickness, weakness and diseases of many kinds occur in every society. 2000 years ago, medical care was not well developed and many sick people died. But even today, with sophisticated treatment available in most cities, there is a 100% cumulative failure of medicine - everybody dies in the end. And so did every person who Jesus healed (including the three people who were raised from the dead).
The purpose of Christ's healing ministry was not to stop all sickness or to prevent death. Indeed, despite many healing miracles, many more people were not healed. When Jesus refused to do miracles in his home town of Nazareth, He reminded then that healing is not a right for the people of God to command (Luke 4:23-27), but a sign of God's love and eternal salvation to people who were helpless. Jesus embodied that compassion because He is God: His healing work was a sign that he had come to save people who are helpless and hopeless (Luke 19:10) ... to give them an eternal hope (John 5:24).
The reason for His coming was to do something far greater than mending broken bodies for a few years - He came to bind up those who are broken-hearted over their sin (Isaiah 61:1) and give them eternal life and security (John 10:28). His healing work was not primarily for the satisfaction of sick people (although people always benefit when God expresses His love), but to glorify Himself as God the Son; and to validate His identify as God's Messiah (Luke 4:18-19).
Suffering of any kind brings distress to our hearts, as well as pain and dysfunction to our minds and bodies. It is natural to reach out to Jesus for help. And we know that He is compassionate, expressing His love in many ways. Church elders are authorised to pray for sick people (James 5:14-16). But we have no right to demand healing or to try to manipulate God into giving us what we want. The greatest blessing we can receive is eternal life, our sins and guilt to be removed and to know that we are accepted in His kingdom. As all the apostles found out, the Christian life is never easy and often we have nothing except His grace - and that is sufficient (2 Corinthians 12:9).