Is anyone among you sick? He should call for the elders of the church, and they should pray over him after anointing him with olive oil in the name of the Lord. The prayer of faith will save the sick person, and the Lord will raise him up; and if he has committed sins, he will be forgiven.It seems to me that our cultural baggage has caused us to see something in this text that is not in it, and to miss something that is.
We tend to see the anointing with oil as integral to the healing. I don't believe that is in the text.
What we miss is that the anointing with oil is a consecrating of the individual to God.
The first time the Bible mentions an anointing with oil is when Jacob sleeps and dreams at Beth-El ("House of God"), and anoints the rock with oil, consecrating the place as God's House. Note that the rock was not sick, and the anointing with oil did not make the rock well. The place was God's.
Later, the utensils in the Temple are anointed with oil. Note that the utensils were not sick and made well by this anointing, but that they were consecrated as being special, chosen, belonging to God. They were God's utensils.
Still later, young shepherd David was anointed with oil by Samuel. David was not sick, and this anointing did not make him well. What it did was consecrate David as being chosen, special, belonging to God. David was God's friend.
The terms "messiah" and "christ" mean "anointed one". Jesus the Messiah was not made well by his anointing; he was made the chosen one by his anointing. His anointing made him consecrated to God. The Messiah was God's presence on Earth.
When someone in the church is sick, he should call for the elders, who will consecrate him to God by the anointing with oil, and who will pray for him, that he might get well. The sick person belongs to God.
Anointing with oil has nothing to do with miraculous gifts, and everything to do with consecrating the anointed one for God's possession.
Accordingly, it might still serve a purpose in the post-miraculous age of Christianity.