The concept of "inflating debt away" is an assumption that wages match inflation while debt stays static. This is a fair assumption in low inflation times, but is showing some cracks these days.
One might then ask, do higher-class wages match/exceed inflation more than lower-class wages? This is debatable. But here's some interesting data from the Atlanta FED, where you can track wages by quintile, education, "skill", hourly vs. non-hourly, etc. Make your own conclusions.