About 80+% of people join the military for money, college, and other benefits. The well-off people don't need the military for that. So, a volunteer military naturally selects for a make up of lower classes to be sent to die overseas to largely protect wealth of upper classes.

If there was a lottery, pushback from casualties would come from more people in upper classes that could cause real problems for politicians and generals. Could even be their own kids sent there. Switching to a "volunteer" military in an increasingly-shitty economy sweeps lots of their problems under the rug. ;)