"When a person writes a reference letter, it is supposed to include both strengths and weakness of the job candidate. This is sensitive information that is necessarily sent directly to the intended recipient."
My thought on this is: if you are looking for employment or new clients, you are going to list references that you know will speak somehow good about you... Think of it this way: if you are going to date a girl, you will most likely introduce her to people who like you, and not people who hate you or you hate ...
"If you require the letter to go through an unknown / untrusted third party on the Internet, the person writing the letter will necessarily water down their criticisms for fear of the letter being seen by unintended eyes, and for fear of liability."
That will happen regardless. If I receive a request for recommendation for an ex employee of mine (let's name him Joe) who was not very good, this means, Joe is looking for employment. I have no guarantee that the letter will not be seen by unintended eyes (or Joe himself), I will never know, and I can't ask the requester... so I will moderate my review anyway. Unless I have some kind of grudge against Joe (in which case Joe would NOT include me as a reference...) I would do a fair review (regardless of who's going to be reading it) and maybe help him out getting a new job without lying or exaggerating...
"Going through a third party may increase convenience, but it decreases the actual value of the reference."
This is true but relative. Maybe it will be decreased a little bit, but at least the recruiter will see the good things about the candidate, and that will help speeding the decision making process up a little bit.
We're very happy that our application is being tested and evaluated, that helps us improve!