There are things suffering does. Paying for sins is not one of them. Only the shedding of blood can obtain forgiveness and forgiveness is the only way sin can be taken care of. It CANNOT be paid off because the wages of sin is death and we cannot pay that penalty.
Suffering produces character qualities in us.
Romans 5:1-5 Therefore, since we have been justified by faith, we have peace with God through our Lord Jesus Christ. Through him we have also obtained access by faith into this grace in which we stand, and we rejoice in hope of the glory of God. Not only that, but we rejoice in our sufferings, knowing that suffering produces endurance, and endurance produces character, and character produces hope, and hope does not put us to shame, because God's love has been poured into our hearts through the Holy Spirit who has been given to us.
Suffering teaches us compassion for each other and gives us the ability to comfort others who are suffering.
2 Corinthians 1:5-7 For as we share abundantly in Christ's sufferings, so through Christ we share abundantly in comfort too. If we are afflicted, it is for your comfort and salvation; and if we are comforted, it is for your comfort, which you experience when you patiently endure the same sufferings that we suffer. Our hope for you is unshaken, for we know that as you share in our sufferings, you will also share in our comfort.
There is NOWHERE in Scripture, however, that teaches that suffering cleanses or purifies us from sin.
I gave you many Scripture citations about the value of suffering and Christ’s own words. I’m sorry that’s not enough for you.