For a correct understanding of healing and Isaiah 53:4-6:
The belief (referred to as "the belief" below) that God has already healed (in the sense that He has already forgiven our sins), and no longer needs to heal today, is incorrect because of a misunderstand of Isaiah 53:4-5 (see below).
1. Verse 53:4 "he took up our infirmities and carried our sorrow"
According to "the belief" this verse refers to the cross. This is not correct. The correct understanding of this verse is given to us by Matthew himself in Matthew 8:16-17 (see below)
By the context it is clear that Matthew means this verse refers to the actions of Jesus before the cross!
This also indicates how to understand the entire verse 4: the prophet is telling us how we can identify the Messiah. He would heal us and share our grief, but we would nevertheless be considered a false prophet.
2) Verse Isaiah 53:4 "with his stripes we are healed"
Because of a misunderstanding of verse 4 "the belief" holds that this phrase confirms that Jesus died for our sickness. It does not.
"with his stripes we are healed" does not refer to sickness. Here are the reasons:
2.1. "stripes" (see Hebrew below)
Jesus suffered stripes because, according to Deuteronomy 25:1-3 (see below), this is the punishment for sin. So the question is: is sickness a sin?
If not, then "with his stripes we are healed" cannot be referring to sickness. Sickness is not a sin and so phrase does not refer to sickness.
2.2. What does "with his stripes we are healed" refer to?
This is speaking of being healed from the disease of the soul called sin! In Mark 2:17 (see below) Jesus refers to the sinner as being sick, and being healed by repentance.
3. Verse 53:6 "We all, like sheep, have gone astray"
Both verse 4 and verse 6 provide the context in which we must understand verse 5 (we have already dealt with verse 4).
In verse 6 Isaiah explains the reason for the cross: because the sheep went astray, not because they were sick! So God laid our sin, not our sickness, on Jesus.
So by the above reasoning it is clear that Jesus did not suffer and die to heal our bodies. This was also not necessary. God has been healing since old testament times, and even raised people from the dead before Jesus died on the cross (1 Kings 17:22).
4. Further "common sense" reasons
4.1. The belief that God healed us (once and for all) on the cross does not make sense
Why would God put the healing of our bodies (something that is not eternal) on the same level as the healing of our soul, which is eternal?
4.2. The fact that we are not healed (in body) completely when we become Christians is obvious.
The belief asks us to suspend disbelief. This is an incorrect understanding of faith which is a trust in the presence of evidence, not blind belief in the face of contradicting facts.
5. But Jesus did die for our sickness!
Yes, indeed, it is not wrong to say that Jesus died to heal us! Just like one day we will be without sin, we will also be without sickness. This is the result of the cross. Why?
Through the fall, both sin and sickness came into the world. But note: the fall was a sin, not a sickness! So sickness came through sin. So the root of the problem is sin.
Jesus dealt with the root of the problem with his work on the cross. This makes it possible for God to forgive our sin, and remove all the results of sin, which includes sickness and natural disorder.
Isaiah 53:4-5 (King James Version)
4 Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted.
5 But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed.
6 All we like sheep have gone astray; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all.
Isaiah 53:4-5 (New International Version)
4 Surely he took up our infirmities and carried our sorrows, yet we considered him stricken by God, smitten by him, and afflicted.
5 But he was pierced for our transgressions, he was crushed for our iniquities; the punishment that brought us peace was upon him, and by his wounds we are healed.
6 We all, like sheep, have gone astray, each of us has turned to his own way; and the LORD has laid on him the iniquity of us all.
Matthew 8:16-17 (NIV)
16 When evening came, many who were demon-possessed were brought to him, and he drove out the spirits with a word and healed all the sick.
17 This was to fulfill what was spoken through the prophet Isaiah: "He took up our infirmities and carried our diseases."
Deuteronomy 25:1-3 (NIV)
1 When men have a dispute, they are to take it to court and the judges will decide the case, acquitting the innocent and condemning the guilty.
2 If the guilty man deserves to be beaten, the judge shall make him lie down and have him flogged in his presence with the number of lashes his crime deserves,
3 but he must not give him more than forty lashes. If he is flogged more than that, your brother will be degraded in your eyes.
Mark 2:17 (NIV)
17 On hearing this, Jesus said to them, "It is not the healthy who need a doctor, but the sick. I have not come to call the righteous, but sinners."
This article is largely a summary of the following text.
Hebrew meaning of "stripes": In Isaiah 53:4: "And with His stripes," the word used for "stripes," in the Hebrew, is "chaburah," Strong 2250. It is in the singular, and it literally means, "a bruise," the result of a blow on the skin (this was quoted from here).