I think you're going to find out your assumption is incorrect. Some that apply to USAFA and USNA
may be doing it for the reasons you stated, but I think the majority are doing it for the opportunities/jobs afforded by those other branches -- ie flying in the AF, SEALS/subs in the Navy, and don't forget the Marine Corps. I say this because at each of the MOC interviews my DS attended, the numbers of those applying to the USNA far outweighed those of the other 3 branches because
a lot of candidates wanted the Marine Corps. I couldn't believe how many candidates expressed their desire for the Marine Corps, so competiton in our state/district is much higher for the USNA. That also seems odd since Kansas has 2 army bases -- Fort Leavenworth and Fort Riley -- and 1 air force base. No naval bases in the center of the country!