The protestant, reformed view, in a nutshell follows along these lines: Christ died and paid for all our sins legally. That is, even though I am still a sinner, I am declared guiltless by God because his wrath was satisfied by being poured out upon Jesus on the cross instead of us (provided, that is, we put our faith in that fact). Eventually some people made the logical extension that if Christ took our curse upon himself, we are healed by his stripes and therefore anything to do with the curse has also been taken away (again, provided we believe). Pain, poverty, suffering, etc., are all a part of that curse. If the curse is gone those consequences of the curse are gone as well.
Reformed protestants claim that Isaiah 53:5 speak only of our salvation from our sins. 1 Peter 2:24 confirms that salvation is definitely in mind here but verse four is used by Matthew to explain why Jesus was healing so many people. It reads:
And when Jesus entered Peter's house, he saw his mother-in-law lying sick with a fever. He touched her hand, and the fever left her, and she rose and began to serve him. That evening they brought to him many who were oppressed by demons, and he cast out the spirits with a word and healed all who were sick. This was to fulfill what was spoken by the prophet Isaiah: “He took our illnesses and bore our diseases.”
(Matthew 8:14-17 ESV)
So is it unreasonable to apply this understanding to verse 5b as well?
There is always the propensity for reinterpreting the facts to fit our perceptions, the Reformed and Charismatic theologians not exempted. One interprets this passage to only refer to salvation and the other to both salvation from sins and disease (and sometimes poverty). But it is clear from the testimony of Scripture, the Church and all of history since Jesus rose from the grave that God heals but not all the time. That people are sometimes delivered from their suffering but not usually. That poverty is a fact for most people in the world, many of them Christian. So one weakens God by claiming miracles ceased after the Apostles (even though there is not biblical testimony of this and Church history clearly denies this) and that the above passages from Isaiah doesn't speak of physical healing and the other group equally puts God in some kind of theological box by insisting everyone is suppose to be healed and that there is no room for suffering in the Christian. I am painting with a broad brush here and representing two extremes, but extremes resultant in a misunderstanding of Scripture or a tenacious clinging to one's system.
The fact is God does heal and sometimes heals through other people. But it is equally true, and more often the case, that God chooses to use suffering to demonstrate his strength and grace through us as Paul tells us:
But he said to me, “My grace is sufficient for you, for my power is made perfect in weakness.” Therefore I will boast all the more gladly of my weaknesses, so that the power of Christ may rest upon me. For the sake of Christ, then, I am content with weaknesses, insults, hardships, persecutions, and calamities. For when I am weak, then I am strong.
(2 Corinthians 12:9-10 ESV)
If we would but look at the history of the Church we would see that, for the majority part, the poor, suffering and destitute were the ones God used the most and to the greatest extent. Not that he didn't use others, but if being free of pain and suffering and poverty was proof both of God's favor and the persons spirituality, then there were truly not many holy people whom God favored throughout the time until the present day.
This fact, that God uses the weak, lowly and despised of the world, is exactly why, after the great persecutions ended (for the most part and for the time being) with Constantine, many men and women chose what is sometimes termed "a white martyrdom" by withdrawing to the uninhabitable regions of the dessert into monasteries or a life of complete solitude as hermits. They knew the world held too great of an attraction for them and without the fire of persecution to burn away the dross and drive deeply a wedge between them and world they would be lost unless they took desperate measures. It is too bad Luther and others didn't understand this before they started destroying monasteries and proselytizing their confused inhabitants away into the hailstorm of the Reformation.
This doesn't mean one must become a hermit or a monk in order to die to self and the world. The monastics would be the first to admit that they withdrew precisely because they were too weak to stay in the world but not of it. But this suffering can come in many ways besides monasticism and persecution. It can come through poverty, marriage (don't laugh), having children, sickness and disease (both temporary and permanent), fasting and so on. The source of suffering is ultimately between God and the person, but let's not forget that God is both desiring our sanctification and is at the same time infinitely creative. So don't be surprised when suffering comes form the most unlikely and least sought after directions.
Am I saying you should always seek suffering? No. Paul spoke of being "content" (Ph'p 4:11-13). So there is that. But sometimes our desire for holiness and closeness to God takes on a more proactive approach. Sometimes we need to force our flesh into submission (1 Cor. 9:27). Sometimes we need to flee youthful lusts. Sometimes we need to run to danger instead of from it, embracing the suffering and pain as gifts from an almighty, loving Father. Yes, he can heal. But sometimes he doesn't want to. Sometimes we need to not want him to.