To the OP and others that may benefit in the future:
It should be uncontroversial that a worthy goal for recruitment is for the demographics of our enlisted corps of the military to closely resemble the demographics of the country. It should then follow that the demographics of the officer corps should ideally resemble the demographics of the enlisted corps. These goals can provide challenges to recruitment for a number of reasons.
A Letter of Assurance or LOA is one tool available to the academies to help them meet their class composition goals.
If we imagine the appointment process as each academy owning a fleet of 24 busses each holding 50 people (for a 1200 class size total) then we can make the following assumptions about the assignment of each bus as it is dispatched (by admissions) to go around the country and gather the desired class. (The numbers don't matter and it is a bit more complicated than this but it may help you understand the LOA better).
2 busses will be dispatched to gather athletes that the coaches desire
2 busses will be dispatched to the Active Duty Military to gather enlisted members
2 busses will be assigned to gather African Americans
2 busses will be assigned to gather Hispanics
2 busses will be assigned to gather Asians
3 busses will be assigned to gather other Under-Represented Minorities (URM)
1 bus may be assigned to gather extremely scholastically gifted candidates
10 busses will be assigned to gather other fully qualified candidates
It is also desirable that each bus contain a certain percentage of females and have candidates from all of the geographic areas of the country. Again the numbers/ratios are unimportant for this exercise and they change over time.
The 10 imaginary busses for "other fully qualified candidates" are pretty easy to fill year over year. All of the other busses can present challenges.
The LOA is like a letter from the bus dispatcher (admissions) that says we think you would fit nicely on one of the busses we have and we will give you a ride back to our academy IF you complete certain requirements AND you obtain a ticket to ride. The "tickets" are called nominations and are controlled by various sources as defined by law. The LOA is really only needed to help overcome the challenges presented in filling some of the historically harder-to-fill bus seats.
You can imagine that if you have an LOA but no nomination or "ticket" whether or not they can "find" a nomination source for you is highly dependent on if there are any seats left on the bus they were hoping to assign you to. If that bus is already full, it is probably unlikely, just know that it is not personal. If the bus is still empty...well, maybe they can use a discretionary nomination. It would be logical to assume that the more LOA that are issued, the less likely, in general, it would be to "find" a nomination for any individual LOA holder that did not earn one on their own.
For a candidate that doesn't hold an LOA the process is kind of reversed. The dispatcher says "if you want to come here, go get a ticket (nomination), and then we will select which of the 10 ticket holders from your neighborhood (or nominating source) get to ride."
The worst two parts about the LOA are the impression it can give to candidates that DO NOT receive one and the impression it can give to those that DO get one. Remember, as soon as you take the oath, not one person you come in contact with will care whether you had an LOA or not, (unless you make it a point to tell them...then they will likely care a great deal, but you might not benefit from their "caring"). If you think in terms of the exercise above, perhaps the 'luster' of the LOA is not quite as bright and shiny as you thought it was.
I would like to offer the same advice I have given my son since he first desired to be selected for something. Be the obvious choice. If you want to be Class President, Captain of the chess team, 1st chair in an orchestra, hired for a position, or a varsity letter winner, find out the selection criteria and become the obvious choice. Let everyone else compete for 2nd place, your only competition is with yourself. You should always be asking yourself some version of "Is that the best you got?" If you have an LOA, nice, great, congrats...now be the obvious choice for a nomination. No LOA? Be the obvious choice.
If your intermediate goal is attending an SA, it should be related to your end goal of being an incredible officer. If so the criteria for selection can be pretty well inferred from each SA's class portrait or profile. Remember, don't compete for the average place or "meet the mean". Be the obvious choice.
FWIW my son fit squarely on the "other fully qualified candidates" bus, did NOT receive an LOA, was NOT selected for NASS but was fortunate enough to receive a principal nomination USNA and apparently won the slate for another.
Good luck and work towards your goal every single day.
Be the obvious choice!