As far as i remember from actual academic analysis and reshearches more active military members cited patriotism/duty etc as the reason they joined than benifits and dept etc (smalish difference in those numbers) with the disparity between those numbers being way bigger in actual active troops and marines and demographic wise poorer layers of society or minorities arent overrepresented and if anything the middle class/middle-upper class is slightly overrepresented with the entire demographic and income background being almost indistinguishable from the police.

From what I can tell, this argument comes from a 2008 study done by The Heritage Foundation, which imo has some major issues, and was put out by a right-wing think tank that openly pushes for privatizing the VA.

This 2018 RAND study probably gives a bit more accurate view of why people join. While there is a mix of reasons cited, economic factors do seem to play a major role:

Soldiers stated that a desire to improve their current and future prospects helped motivate them join the military. In particular, many soldiers sought to gain access to the military’s benefits (n=25; 32 percent). These particularly included health care, tuition assistance during service, and the GI Bill. Some participants saw these benefits as a lifeline; one single parent said she joined “just because I had my son and I needed the benefits, I guess you could say” (CMF92). Others used the Army to look to the future and create a better life after military service:

The Army can provide me with great education benefits, great career benefits later on. So... why not start that and do that, instead of just working at some dead-end job that’s only paying minimum wage, maybe $10 an hour when I can go and get fantastic benefits, all that.

(CMF13) A quarter of soldiers (n=19; 24 percent) joined for the stable pay, knowing they “needed to make money” (CMF92). Some soldiers saw joining as an opportunity for short-term employment, while others sawthe prospects of a steady career: “After I weighed the pros and cons I was like, well, why not, and if I stay in for 20-plus years [I can] retire at 40. So it seemed like a good deal to me, especially in the economy we’re in” (CMF68). Some soldiers (n=17; 22 percent) joined the military to get away from some aspect of their prior lives. In some cases, this was simply escaping a hometown without prospects, but in others, soldiers described leaving bad family situations or unsafe environments.