They care about the content of the letter most importantly. You're assuming the personal feelings of the people reading the letters directly reflects whatever you read online about that school.
For every school you apply to, there will be a combination of letters, of which their content will have the greatest impact on the readers. The greater number of variations, the lesser likely you are to hit that combination. The odds of you picking the best combination of five out of nine, for every school, is astronomically low.
You can have this complex letter arrangement plan all you want, I just don't think its offering you a great advantage over someone who has the standard 2 science, 1 non science, 1 doctor, 1 community, of which are all well written. That person has all of their bases covered to, they just don't have three of each.
Hopefully someone with adcom experience can chime in on this, but this method of letter gathering is seemingly a lot of work for very little, if any reward.