If one sins then sickness can be allowed by God until one repents. Repentance is a gift which God is under no obligation to grant. What you are saying is anyone can sin and never be sick as a consequence and not have to repent to be healed. Paul is quite clear that sin can get one dead if they do not repent in 1 Corinthians 5:5. Acts 5:1-10 is quite clear as well. They were not even given an opportunity to repent. I guess you are saying Ananias and Sapphira just lacked faith.James 5:14-15
New International Version (NIV)
14 Is anyone among you sick? Let them call the elders of the church to pray over them and anoint them with oil in the name of the Lord. 15 And the prayer offered in faith will make the sick person well; the Lord will raise them up. If they have sinned, they will be forgiven.
Death, decay and sickness entered the world when the fall occured. You and I and everything else in this world is in a state of "decay".
It was SIN in 1 Corinthians 11:27-34 that caused some to be both sick and dead.
I will say if one is in sin faith for healing is not possible until repentance is sought and granted by God.
As for James 5 there certainly is a connection between sin and sickness. The sickness is not always because of sin but obviously may be from what is said. It is also obvious that God will grant the gift of repentance if sin is the reason and they will be healed.