Sorry for the late reply. Life has been very busy here.
In the US I have noticed most Catholics have a Mass at the time of their burial and it is usually called a funeral. In some places the burial is done very quickly, often within 24 hours, and the funeral and burial often do not include a Mass. Masses will be said for the person who died, often many of them, but it is rare in some places to have a priest there for the actual funeral and burial. It just isn’t possible in many rural areas of the world where embalming doesn’t happen and one priest covers several towns.
Here, in MO, I attend several funerals because I am the altar server coordinator at two parishes. If my servers are on the altar, I make sure I am in the church with them. Over the last six years I have attended multiple funerals—nearly all had a Mass of Christian Burial at the same time. The Mass most certainly is for the repose of the soul for the deceased. It is a very powerful prayer. The entire funeral, though, is for the living. It is a source of comfort for those of us left behind. The priests I have been blessed to be with during these funerals, which usually do include a Mass, have all stated that the funeral is a time to reflect on the hope of Christ and ask for comfort in that hope. It is a time for the family to be surrounded in love and comforted. It is most certainly is for the living as they pray for the loved one they lost.