If everyone should follow Paul’s instructions for disfellowshipping as you state, then why not an “appointment?”
The appointment was not an official appointment. Paul, obviously accepted Mark and saw his value, for he mentions him as a loyal servant of Jehovah.
The bible states to confess your sins to one another, not just the “elders.”
You have misread that scripture. A few verses back, James was talking about going to the elders. So following the line of logic, the confessing the sins with one another referred to confessing the sins to elders not to just anyone.
Here is the scripture:
13Is any one of you in trouble? He should pray. Is anyone happy? Let him sing songs of praise. 14Is any one of you sick? He should call the elders of the church to pray over him and anoint him with oil in the name of the Lord. 15And the prayer offered in faith will make the sick person well; the Lord will raise him up. If he has sinned, he will be forgiven. 16Therefore confess your sins to each other and pray for each other so that you may be healed. The prayer of a righteous man is powerful and effective.
Nowhere in the bible does it place elders in a privileged class to hear your “case.”
In the Corinthian congregation, who were responsible for removing the wrongdoer from the congregation?
1 Corinthians 6:4, 5 says "4If you have legal disputes about such matters, why do you go to outside judges who are not respected by the church? 5I am saying this to shame you. Isn't there anyone in all the church who is wise enough to decide these arguments? "
Galatians 6;1 says "1Dear brothers and sisters, if another Christian[1] is overcome by some sin, you who are godly should gently and humbly help that person back onto the right path. And be careful not to fall into the same temptation yourself. "
Obviously someone had to hear that persons "case". Who better to do it, than those that had the appointment as elders.