Where I’m from in the South, having a notably Southern accent is a tell that you grew up in a lower class family and area, and all that goes with it (like having less education). Obviously it doesn’t mean you’re stupid, but regarding education and workforce readiness (a lot of Southern communities have very low workforce participation rates, and almost no white collar jobs outside government) it’s a Bayes rule thing.

So I would dispute the causation here - it’s not the accent itself that reduces wages, but being from a poorer family without much exposure to the corporate world that does.

Though of course, even aspects of the mild accent I do have invite unwanted attention sometimes, so it’s no surprise people with much stronger accents would code switch and conceal it.