There is a little uncertainty about the range checks if the Army is the first level of command-I used the worst case.
Range check is done on all levels. As I can see range modifiers in your tables are incorrect.
Ex.
Corps range 5 rg mod = abs(5-5)/1 = 0
Army range 10. rg mod = abs(10-5)/2 = 2
AG range 15. rg mod = abs(15-5)/3 = 3
HC range 30. rg mod = abs(30-5)/4 = 6
etc..
Bottom line is the unit reporting directly to the army has a greater chance of passing the initiative check than the unit reporting to a corps - all else being equal.
Yes, having very high rating commander very close to
all of your units makes upper levels obsolete. This is obvious and doesn't require any math.