Good post, and here's some data to back up what you're saying.

Rich Man’s War, Poor Man’s Fight?: Socioeconomic representativeness in the modern military

Historically, the American armed forces were disproportionally drawn from lower socioeconomic backgrounds. A transition toward a smaller and more selective military has changed this tendency. Since the armed forces do not gather data on recruits’ family income, previous studies relied on geographic data to proxy for economic background. We improve on previous literature using individual-level data from the National Longitudinal Survey of Youth 1997 and study population representativeness in the years 1997–2011. We find that recruits score higher than the civilian population on cognitive skill tests, and come from households with above average median parental income and wealth. Moreover, both the lowest and highest parental income categories are under-represented. Higher skill test scores increase enlistment rates from lower- and middle-income families while decreasing them for high income families. The over-representation of minorities in the military has declined in recent decades. Non-Hispanic White casualties are now over-represented in Iraq and Afghanistan.

79% of Army recruits reported having a family member that served. For 30%, it was a parent.

In terms of social class, Kane (2006) found that people who serve in the military come from more well-off neighborhoods than those who have not joined the military although the economic elite are underrepresented in armed service (Heritage foundation of all places did this study)

Importantly, it was historically the poor who fought in America's wars. But now it's the children of the once poor but now middle-class who largely fight in wars. They're treating the military like college or a trade.