Part of the importance of Anointing of the Sick is that it is preparing the afflicted for life after death
The sick are told what will happen, allowed to give penance and prepared for the laying of the hands and the blessing of the oil
Before surgery, a patient is told what is going to happen, then they can ask questions.
The cleansing of the person and the tools before a surgery are like the laying on of the hands and the blessing of the oil because they are preparing the person for the final step
Also, during surgery, people are healed and during anointing of the sick, people are healed as well