Are people with 125+ IQs enlisting? Not for the most part, but almost none of the 75 IQ people are enlisting, and they cause a wild disproportion of the problems in society.
There are a lot of advantages to living on base, but this thread is pretending that the military has its shit together in ways that it absolutely does not. "All the kids will be well-fed and socialized" is bizarrely out of touch, specifically. There are functioning gangs on some larger military installations. Troops PCS every few years, making it difficult for kids to establish social groups. Most bases have a unit of MPs basically acting as child services.
I'd think a better place to look for filters would be entire schools -- BRAC has caused the closure of many schools, but I don't know how they select which schools to target for closure. I know of at least two larger bases which have no schools (students are bused to local civilian schools) but I know others who have kept their schools despite a lower overall population of families.
If they're in that low IQ tail and they go through the hoops for a waiver, you've just selected for a modicum of conscientiousness.