I encourage searching and reading through threads, as various options for postgraduate education, law school, varsity sport opportunity,etc., pop up in past series of related questions and comments.
In general, I would say all the SAs have a primary mission, which is not to produce lawyers, but once the initial objective is achieved and requirements fulfilled, then there are many great options for post-grad education and career transitions out there.
As for the USNA and law school, the Navy gets many of its lawyers through direct commission, meaning they recruit from law school graduates who attended civilian college and law school. USNA is meant to produce warriors, unrestricted line officers, meant to serve and command in the Fleet and Corps. The JAG Corps is a restricted line community, meaning they may command ashore and only at JAG units.
There is a path from Navy unrestricted officer career paths to the JAG Corps. Junior officers, regardless of commissioning source, generally go to sea in their respective warfare career path. After earning their warfare quals, and after a certain amount of time, they may apply for a lateral transfer from unrestricted line to restricted line, say from surface warfare to JAG. If they are approved and have been accepted to law school, they are released to go. This is the Navy's LEP, Law Education Program. VERY competitive, and only a few are chosen each year. Navy pays for the law school. We sponsored a USNA '00 midshipman, high achiever at USNA, excelled as a surface warfare officer during his initial sea tours, applied to LEP, went to UVA Law, now serving as a JAG. He is head and shoulders above his direct commision peers and highly regarded by senior JAGs because of his warfare experience. I remember him talking about it as a midshipman, but he knew he had to hit the deck running and focus on his surface warfare career to position himself to play for the JAG shot.
It's something that can be done, way down the road, but I believe it's more important to focus on best fit at SA first coupled with best fit for immediate post-commissioning career paths. Make a well-thought-out choice there, and other opportunities will unfold. There are many naval officers who have transferred out of their warfare qualifications to continue serving as Public Affairs, Intelligence, Medical Corps, Engineering Duty Officers and others. A caveat: "the needs of the Navy (any service)" will trump all.
Lastly, I wouldn't worry too much about graduation rates as a decision factor. The SA's are so far above "regular schools" in % graduating, they are in a class by themselves.
Congrats on having such a choice. It's hard to leave a choice by the side of the road, knowing there are no do-overs once the other path has been chosen.