I think it is important to the organization that they get an 'organizational' man as presiding overseer.
A few years back our presiding overseer moved to another congregation and it was interesting to see the hassling for the position that went. I know was in the running myself but am sure that I didn't fit the ideal 'company' man image.
However, I was approached by a couple of elders and asked who I thought should be presiding overseer; elder X the real company man with no people skills, and certainly not an inspirational sort of person, or elder Y, a real 'people person', caring and loving but total disorganised. My answer was "we can help organize brother, Y but you can never make a non people person caring and loving, go for the spiritual not the company man.
Remembering, it is the CO that has the final say in these sort of things but that he does take opinion from the BoEs, who do you think got appointed? You guessed it brother X.
He then gangs up with his cronies, and within a year they have made life so difficult for brother Y that he ends up leaving the congregation after one of the most acrimonious elders meetings I have had the misfortune to attend.