People of faith do go to God with all such requests, when they find themselves in those circumstances, yet their faith and trust in their God almighty do not waver, when at times these requests of healing of physical deformities are not answered. In spite of this they understand their God and know that He does exist. He is not supposed to be available for us like a Superman at our every request. He has His own plan for us and is uncomprehending to our finite mind.
Faithful understand that if God was to agree to our every request than each one of us would ask and pray that we may never die but continue to live for eternity. We can also ask Him to heal every disease and infirmity of all people in this world. But His plans are not our plans.
Isaiah 55:8 “Indeed, my plans are not like your plans, and my deeds are not like your deeds, 55:9 for just as the sky is higher than the earth, so my deeds are superior to your deeds and my plans superior to your plans.
What is best for us is not always physical wholeness. Paul the apostle prayed to have his "thorn in the flesh" removed, but God said, "No," because He wanted Paul to understand he didn’t need to be physically whole to experience the sustaining grace of God. (2 Corinthians 12:7-10).
From testimony of Joni Eareckson Tada on modern-day miracles, she says, "Man’s dealing with God in our day and culture is based on His Word rather than ‘signs and wonders’"
That answer, in short, would be something like this: "God can heal amputees/ physical deformities and will heal every one of them who trusts Christ as Savior. The healing will come, not as the result of our demanding it now, but in God’s own time, possibly in this life, but definitely in heaven. Until that time, we walk by faith, trusting the God who redeems us in Christ and promises the resurrection of the body."
Why such miracles were common earlier.
In the thousands of years of history covered by the Bible, we find just four short periods in which miracles were widely performed-the period of the Exodus, the time of the prophets Elijah and Elisha, the ministry of Jesus, and the time of the apostles. All the type of miracles that are mentioned in the question were performed during these periods.
While miracles occurred throughout the Bible (and they still happen), it was only during these four periods that miracles were "common." During these periods, God used miracles and direct communication with people in order to reveal to them His character and nature, as well as His plans and commands.
When Jesus came to earth, He also performed miracles to prove that He was indeed the Son of God and to foster belief in Him (Matthew 9:6;John 10:38). After His miraculous resurrection, He enabled His disciples to continue performing miracles in order to prove that they were truly His, so that people would believe on Him who sent them.
Therefore we can say that God has already spoken, and His words have been miraculously kept for us down through the ages. Now we need no further miracles to “validate” the Bible. In His perfect "Word" is everything we need “for doctrine, for reproof, for correction and instruction in righteousness” (2 Timothy 3:16). The Bible is complete and is perfectly able to make us “wise to salvation through faith in Christ Jesus” (2 Timothy 3:15). We need nothing more, and we are not to seek extra-biblical revelations. To do so calls into question the efficacy of Scripture which God has declared to be sufficient.
Prophet Habakkuk said: “The just shall live by his faith” (Habakkuk 2:4). God does not give His people a continual chain of miraculous signs; He expects them to trust what He has already done, search the Scriptures daily, respond to the Holy Spirit within, and live by faith, not by sight (Matthew 16:4;John 20:29).