Only de jure, not de facto. The de facto Catholic Cathedral is St. Mary's Pro-Cathedral. The Pope has never removed the Cathedral designation from the Cathedral of the Holy Trinity ("Christ Church Cathedral").
True enough...
How does this factor into the column? Many pilgrims who come to the beautiful cathedral are caught up in the worship of the relic. That does not diminish the church. The column is meant to remind us all to focus on the only One worthy of our devotion.