Mike,
Back in the late ' 50s a country club in my neck of the woods was forced to give up some of it's land for a new interstate highway, so they asked their original architect, RTJ Sr., to come up with a solution for them. After sussing it all out he, along with Gene Sarazen, had a meeting with the membership and told them that they both felt the remaining property could be turned into an excellent 9 hole course or a mediocre one of 18 holes. Gotta admire their honesty.
The club had Jones build them the 18 holes, he and Sarazen were right, and I don't believe that anyone involved even gave a thought to settling on a number between 9 and 18.
The 'need' to make some less than stellar holes to reach the 'magic' number of 18 probably has something to do with the number of members a club has, wants to have, or feels it needs to keep its ledger in the black. Most 18s around here have 300 +- members, and that number of holes keeps everyone happy. The one 9 holer I know of that has about 300 members is a zoo for the players and the staff.
On the public side it's mainly a game of $s.