Then what is the purpose of the SAs sending copies of the LOAs to the MOCs?
Exactly!
DS's experience was that when he made contact with the MOC staffers with some final questions he asked if he needed to include a copy of his LOA in the application.
Every MOC staffer immediately changed tone, one checked and mentioned they already had it in his file. The other two thanked him for letting them know, and yes, to include a copy.
All three said "we'll definitively be scheduling an interview with you" or similar as soon as the LOA came up. IE: The existence of an LOA appeared to bypass an initial screening review.
DS's read: It's all in the attitude you bring to the discussion. If you are sincere and come across as just wanting to do the best job at the application & interview you can, they seem OK with it. Bring an expectation of entitlement, or attitude, and it could backfire.
And the LOA does somewhat let them know you should be (on average) competitive for at least once academy. And that comes through in how the MOC staffer verbal body language changes on the phone. Apparently, sorting through many, many non-competitive applications is a major time issue for them, especially senator teams.
How that information is used in the interviews, is it passed to the committees, etc, unless they tell you there is no way to know. And the advice previously given to approach the interviews as if you do not have an LOA seems the best approach. (Especially if you are applying for more than one academy)
There is an issue with some MOC's that an LOA may mean you are not considered for nomination for other academies, especially if your LOA for your stated first choice. At least one of our senators does the interviews by branch, running multiple committees in parallel.