Why is the Mormon Church obsessed with statistics such as visiting teaching, home teaching etc.?
What makes you think that the church is obsessed with statistics? In order for any organization to manage its affairs it must know what is going on. How would the bishop know what Priesthood and Relief Society assignments to make if he did not know the performance level of the home teachers and visiting teachers? How would the church know when to build new chapels to meet the demand of the members if it didn’t know how many members lived within a given area? How would the church know where to build temples if it had no idea of the faithfulness of the members within a given area? How would the church know how many missionaries to call to any given mission without knowing how effective the missionary work was in any given area? How would the church know when to divide a Ward or create a new Stake without knowing the number of members and activity level of the members in the ward or stake? How would the church know when to create a Stake from a District in the mission field without knowing the number of members and their activity level in the District? How would the church know if it had the funds to build new chapels and temples without an accurate assessment of the tithing paid? The list goes on and on.
However, to avoid the competition between units that is sometimes generated by comparing statistics of activity levels, the membership and activity statistics of one area-ward, stake, mission, etc. are not shared with other like units. This demonstrates that the church is not obsessed with statistics, but has an active program to avoid such obsessions.