I don't think there's a strong economic argument against multiple Time-Turners -- I can think of a number of reasons why the demand for additional loops might run into diminishing returns pretty quickly. Starting with self-consistency problems -- if the simplest solution to a factoring problem that leverages Time-Turning is "DO NOT MESS WITH TIME", then it wouldn't surprise me too much if the simplest self-consistent solution to more complicated and dangerous tasks that involve self-reference is a mysterious death or incapacity on the first iteration. This would be noticed, and Time-Turner abuse would be avoided. Then there's jet lag, synchronization issues, and any number of other things. More than one Time-Turner would definitely be useful (and desired), but the twenty-fifth wouldn't be anywhere close to as useful as the first.
That being said, I think you present pretty solid behavioral reasons why we can probably assume it's impossible.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: